Empirical star formation laws from the last 20 years are reviewed with a comparison to simulations. The current form in main galaxy disks has a linear relationship between the star formation rate per unit area and the molecular cloud mass per unit area with a timescale for molecular gas conversion of about 2 Gyr. The local ratio of molecular mass to atomic mass scales nearly linearly with pressure, as determined from the weight of the gas layer in the galaxy. In the outer parts of galaxies and in dwarf irregular galaxies, the disk can be dominated by atomic hydrogen and the star formation rate per unit area becomes directly proportional to the total gas mass per unit area, with a consumption time of about 100 Gyr. The importance of a threshold for gravitational instabilities is not clear. Observations suggest such a threshold is not always important, while simulations generally show that it is. The threshold is difficult to evaluate because it is sensitive to magnetic and viscous forces, the presence of spiral waves and other local effects, and the equation of state.

The origin and types of spiral arms are reviewed with an emphasis on the connections between these arms and star formation. Flocculent spiral arms are most likely the result of transient instabilities in the gas that promote dense cloud formation, star formation, and generate turbulence. Long irregular spiral arms are usually initiated by gravitational instabilities in the stars, with the gas contributing to and following these instabilities, and star formation in the gas. Global spiral arms triggered by global perturbations, such as a galaxy interaction, can be wavemodes with wave reflection in the inner regions. They might grow and dominate the disk for several rotations before degenerating into higher-order modes by non-linear effects. Interstellar gas flows through these global arms, and through the more transient stellar spiral arms as well, where it can reach a high density and low shear, thereby promoting self-gravitational instabilities. The result is the formation of giant spiral arm cloud complexes, in which dense molecular clouds form and turn into stars. The molecular envelops and debris from these clouds appear to survive and drift through the interarm regions for a long time, possibly 100 Myr or more, with lingering spontaneous star formation and triggered star formation in the pieces that are still at high-pressure edges near older HII regions.

Star formation occurs in hierarchical patterns in both space and time. Galaxies form large regions on the scale of the interstellar Jeans length and these large regions apparently fragment into giant molecular clouds and cloud cores in a sequence of decreasing size and increasing density. Young stars follow this pattern, producing star complexes on the largest scales, OB associations on smaller scales, and so on down to star clusters and individual stars. Inside each scale and during the lifetime of the cloud on that scale, smaller regions come and go in a hierarchy of time. As a result, cluster positions are correlated with power law functions, and so are their ages. At the lowest level in the hierarchy, clusters are observed to form in pairs. For any hierarchy like this, the efficiency is automatically highest in the densest regions. This high efficiency promotes bound cluster formation. Also for any hierarchy, the mass function of the components is a power law with a slope of around − 2, as observed for clusters.

Triggered star formation in bright rims and shells is reviewed. Shells are commonly observed in the Milky Way and other galaxies, but most diffuse shells seen in HI or the infrared do not have obvious triggered star formation. Dense molecular shells and pillars around HII regions often do have such triggering, although sometimes it is difficult to see what is triggered and what stars formed in the gas before the pressure disturbances. Pillar regions without clear age gradients could have their stars scattered by the gravity of the heads. Criteria and timescales for triggering are reviewed. The insensitivity of the average star formation rate in a galaxy to anything but the molecular mass suggests that triggering is one of many processes that lead to gravitational collapse and star formation.

Young galaxies are clumpy, gas-rich, and highly turbulent. Star formation appears to occur by gravitational instabilities in galactic disks. The high dispersion makes the clumps massive and the disks thick. The star formation rate should be comparable to the gas accretion rate of the whole galaxy, because star formation is usually rapid and the gas would be depleted quickly otherwise. The empirical laws for star formation found locally hold at redshifts around 2, although the molecular gas consumption time appears to be smaller, and mergers appear to form stars with a slightly higher efficiency than the majority of disk galaxies.

Numerical simulations provide an increasingly detailed picture of the build-up of the stellar mass of galaxies, but they remain schematic in their description of the dissipative processes which regulate star formation. The mechanical energy released by mergers, gas accretion, the formation of bound systems and feedback must be dissipated for star formation to occur and proceed. Spectroscopy of warm H2 observations with the Spitzer Space Telescope and the SINFONI spectro-imager at ESO have unraveled an unexpected facet of the energetics of galaxy and star formation. They show that the dissipation processes involve the formation and dynamical heating of molecular gas. I present the physical understanding of the energetics of the multi-phase, turbulent interstellar medium, which arises from the observations and data modeling.

I review what can be learned from studying nearby galaxies about the star formation process. The main interest of these galaxies is that they pose a different regime of star formation and physical conditions than are available in the Milky Way. I discuss how the tracers that we have for determining the star formation efficiency are affected by low metallicity and more bursty star formation in dwarf galaxies. The reduced shielding of the ISM hugely affects the structure of the ISM, in particular the applicability of CO to trace the dense molecular clouds where star formation may occur. I also discuss how the dust emission maybe affected.

This lecture reviews fundamental physical processes on star formation in galaxy interactions and mergers. Interactions and mergers often drive intense starbursts, but the link between interstellar gas physics, large scale interactions, and active star formation is complex and not fully understood yet. We show that two processes can drive starbursts: radial inflows of gas can fuel nuclear starbursts, triggered gas turbulence and fragmentation can drive more extended starbursts in massive star clusters with high fractions of dense gas. Both modes are certainly required to account for the observed properties of starbursting mergers. A particular consequence is that star formation scaling laws are not universal, but vary from quiescent disks to starbursting mergers. High-resolution hydrodynamic simulations are used to illustrate the lectures.

Stars and star clusters form by gravoturbulent fragmentation of interstellar gas clouds. The supersonic turbulence ubiquitously observed in Galactic molecular gas generates strong density fluctuations with gravity taking over in the densest and most massive regions. Collapse sets in to build up stars.

Turbulence plays a dual role. On global scales it provides support, while at the same time it can promote local collapse. Stellar birth is thus intimately linked to the dynamical behavior of parental gas cloud, which governs when and where protostars form, and how they contract and grow in mass via accretion from the surrounding cloud material. The thermodynamic behavior of the star forming gas plays a crucial part in this process and influences the stellar mass function as well as the dynamic properties of the nascent stellar cluster.

This lecture provides a critical review of our current understanding of stellar birth and compares observational data with competing theoretical models.

In this lecture, the general properties of molecular clouds are presented, then the physics of the earliest stages of star formation is introduced thanks to a simplified stability analysis of these clouds. We later compare the outcomes of this analysis with observations of molecular clouds and point out the complex interplay of gravity, magnetic fields and turbulence necessary for the understanding of star formation processes, with a special emphasis on preliminary results from the recent Herschel Gould Belt survey.

In this lecture, we briefly present the main models currently proposed to describe the collapse of prestellar dense cores and the formation of young Class 0 protostars. An empirical evolutionary sequence for the formation of low-mass stars is described. Then, the typical properties of Class 0 protostars are reviewed and the question of their structure at small scales is adressed through the question of circumstellar disks.

We first review the current debates about massive star formation over the last decade. Then we concentrate on the accretion scenario, emphasizing the evidences in favor of it. We study the basic properties of the accretion scenario in the spherical case. In the case of massive stars, the free-fall time is longer than the Kelvin–Helmholtz timescale, so that the massive stars in formation reach thermal equilibrium before the accretion is completed. This is why the history of the accretion rates for massive stars is so critical. We derive analytically the typical accretion rates, their upper and lower limits, showing the importance of dust properties.

We examine the basic properties of the disk, their luminosity and temperature in the stationary approximation, as well as their various components. The results of some recent numerical models are discussed with a particular attention to the effects that favor accretion on the central body relatively to the case of spherical accretion. These effects strongly influence the final stellar mass resulting from a collapsing clump in a cloud. We also show some properties of the pre-main sequence tracks of massive stars in the Hertzsprung-Russell diagram. During the first part of their evolution up to a mass of about 3Mʘ the forming stars are overluminous, then they are strongly underluminous (with respect to the zero age main sequence) up to a mass of about 10Mʘ until they adjust after a slight overluminosity to the main sequence values. We consider some rotational properties related to star formation. The angular momentum has to be reduced by a factor of about 106 during star formation. Some effects contributing to this reduction have been studied particularly in the case of low- and intermediate-mass stars: disk locking and magnetic braking. We also discuss the case of massive stars and emphasize the effects of the gravity darkening of rotating stars that may favor the accretion from the disk of massive stars in formation.

This review covers a variety of topics related to the properties of Pre–Main Sequence stars in star forming regions, young clusters and associations. Some recent developments of theoretical models of PMS evolution are discussed, with emphasis on the role of magnetic fields in low-mass stars and their impact on observable quantities. Critical tests on the comparison between model predictions and observations are presented for stars across the mass spectrum. The issue of the formation and early evolution of massive stars is addressed, with emphasis on clustered versus isolated objects. After a brief historical background on the derivation of the Initial Mass Function, current representations of this quantity are discussed. The issue of the duration of the star formation process is dealt with using the results of age dating methods for young stars, mainly based on the property of Lithium depletion during PMS evolution. A recent analysis of the properties of the stellar population of the Orion Nebula Cluster is presented with the resulting IMF and age distributions. Finally, a discussion of recent determinations of the metallicity distribution of young stars in clusters and associations closes the review.

Short-lived radionuclides (SLRs) are radioactive elements (T1/2 ≺ 200 Myr) which were present in the nascent solar system and are now extinct. While the initial abundance of SLRs with the longest half-lives (T1/2 ≻ 3 Myr) is compatible with the expectations of Galactic evolution models, others have a last-minute origin. 7Be, 10Be, 36Cl, and 41Ca probably originated within the protoplanetary disk from the irradiation of gas and dust by energetic particles accelerated by the protoSun. 26Al and 60Fe were probably synthesized by massive stars and added to interstellar gas which will eventually make up the bulk of our solar system. Identifying the detailed mechanisms of 26Al and 60Fe production and mixing will shed a light on the relationship between the Sun formation history and massive stars.

We briefly review the feedback effects of massive stars, via their stellar winds and supernova explosions, on the star-forming regions in which they were born. We give a few examples, spanning a wide range of spatial scales, from ∼100 pc out to ∼10 kpc: the so-called “Local Bubble” (in reality an open bipolar structure extending on both sides of the galactic disk); the Extended Orion Nebula and its open cavity filled with a hot, MK outflowing plasma; the Great Carina Nebula and its extended diffuse X-ray emission; the 30 Dor region in the LMC and its various bubbles; and the extended, bipolar outflow of the prototype starburst galaxy M 82, influenced by a nearby group of galaxies. We conclude by stressing the similarity of these phenomena across all spatial scales, galactic and extragalactic.