This and the following two chapters present a general introduction to the subject of observing magnetic fields in stars using spectropolarimetry. The three chapters will consider (1) the basic physics of the Zeeman and related effects, direct deductions about stellar magnetic fields that may be made where this effect is detected, and how such measurements have provided much information about the Sun and other magnetic stars; (2) how spectropolarimetric observations of magnetic stars may be modelled, and how such techniques may be used to extract much detailed information about the stellar magnetic field and other characteristics of the magnetized stellar atmosphere; and (3) how other magnetic effects such as the Hanle effect and continuum polarisation may be used to detect fields in a variety of stellar types such as white dwarfs, and how the current body of observational knowledge about magnetic stars may be integrated into a roughly coherent, provisional scenario of field origin and evolution.
In this chapter we survey the physics of an atom in a magnetic field (the Zeeman effect and its relatives), and identify ways in which magnetic effects on the atomic energy level structure may be used to detect and characterise stellar magnetic fields. We survey some of the basic features of magnetism in the Sun. We then describe how the available data may be used to deduce simple averages of various magnetic quantities over the stellar surface (for example, the “mean longitudinal field”) and how such simple field measurements are used to develop and explore the “oblique (dipole) rotator model” of magnetism for a group of middle main sequence stars called the “magnetic Ap stars”.

In this chapter, we examine the question of how spectropolarimetric observations of magnetic stars may be modelled, and how modelling techniques may be used to extract much detailed information about the stellar magnetic field and other characteristics of the magnetized stellar atmosphere.

We start by looking at some recent developments in field measurements in middle main sequence and pre-main sequence stars. Then we consider how other magnetic effects such as the Hanle effect and continuum polarisation may be used to detect fields in a variety of stellar environments such as the solar corona and white dwarf atmospheres. Finally we consider how the current body of observational knowledge about magnetic stars may be integrated into a roughly coherent, provisional scenario of field origin and evolution.

In this chapter I present methods to measure stellar magnetic fields, in particular the regression method used with low-resolution spectropolarimeters and the Least Square Deconvolution method used with high-resolution spectropolarimeters. I discuss the advantages and inconvenients of each method and the various instruments available as of today. I conclude on the best polarimeter to use depending on the science goal and type of studied objects, and provide a short summary of the two ongoing large programmes MaPP and MiMeS.

The stellar internal magnetism is presently poorly known, even we have now some evidence that it plays a crucial role in different stages of stellar evolution. I first recall the helioseismic results coming from the SOHO mission on the deep interior. Then I show how we hope to observe directly or indirectly the deep solar magnetism by the simultaneous detection of gravity modes, acoustic modes and other phenomena. The two following sections compare the different techniques of observation and show the interest of a multichannel resonant spectrometer both for studying the deep dynamics of the core and for putting some constraints on the stellar atmospheric models. The last section describes the DynaMICCS mission submitted to ESA in the framework of Cosmic Vision 2015–2025 and the observations of the coming decade with the GOLF–NG instrument dedicated to the magnetism of the core and to the region located between photosphere and chromosphere.

The objective of this paper is to give a review of solar and stellar activity, from the observationnal constraints to dynamo models. I first review solar observations and insist on the various scales. Then I describe the photospheric magnetic structures (from spots and plages to the magnetic network and internetwork magnetic fields) and the energetic events in the chromosphere and corona, such as prominences, flares and coronal mass ejections. It is mostly photospheric observations (in addition to the results obtained with helioseismolohy concerning the internal rotation) which are providing the important constraints for dynamo models, that are reviewed. However the energetic events can also be used as tracers of solar activity and have a significant impact on earth. Stellar activity is then reviewed, including results on differential rotation. I insist on the comparison with solar properties. I then come back on the constraints these stellar observations bring to dynamo models.

Among the A/B stars, about 5% host large-scale organised magnetic fields. These magnetic stars show also abundance anomalies in their spectra, and are therefore called the magnetic Ap/Bp stars. Most of these stars are also slow rotators compared to the normal A and B stars. Today, one of the greatest challenges concerning the Ap/Bp stars is to understand the origin of their slow rotation and their magnetic fields. The favoured hypothesis for the latter is that the fields are fosils, which implies that the magnetic fields subsist throughout the different evolutionary phases, and in particular during the pre-main sequence phase. The existence of magnetic fields at the pre-main sequence phase is also required to explain the slow rotation of Ap/Bp stars. 
During the last 3 years we performed a spectropolarimetric survey of the Herbig Ae/Be stars in the field and in young clusters, in order to investigate their magnetism and rotation. These investigations have resulted in the detection and/or confirmation of magnetic fields in 8 Herbig Ae/Be stars, ranging in mass from 2 to nearly 15 solar masses. In this paper I will present the results of our survey, as well as their implications for the origin and evolution of the magnetic fields and rotation of the A and B stars.

Whereas the understanding of most phases of stellar evolution made considerable progress throughout the whole of the twentieth century, stellar formation remained rather enigmatic and poorly constrained by observations until about three decades ago, when major discoveries (e.g., that protostars are often associated with highly collimated jets) revolutionized the field. At this time, it became increasingly clearer that magnetic fields were playing a major role at all stages of stellar formation. 
We describe herein a quick overview of the main breakthroughs that observations and theoretical modelling yielded for our understanding of how stars (and their planetary systems) are formed and on how much these new worlds are shaped by the presence of magnetic fields, either those pervading the interstellar medium and threading molecular clouds or those produced through dynamo processes in the convective envelopes of protostars or in the accretion discs from which they feed.

Stars constitute undoublty one of the elementary blocks of the Universe and play as such a central role in determining for instance its chemical evolution. They can be seen as modern physics laboratory from which fundamental processes as diverse as atomic physics or turbulence can be studied and understood. Being able to model accurately their structure, dynamic and evolution is thus of fundamental importance and is the subject of intense research. In this short lecture we will first discuss the basic equations and processes, such as convection, turbulence, rotation, instabilities and dynamo action that are at the origin of the magnetic field observed in stars. We will then present some of the numerical simulations in three dimensions performed in recent years to model such complex objects and their nonlinear behavior, focussing mainly on results obtained with the anelastic spherical harmonic (ASH) code. Using the Sun as a reference star, we wish to gain insight the various magnetohydrodynamical processes that shape its large scale dynamics and magnetism, such as the Reynolds and Maxwell stresses, and the ω and α-effects. We will then extend our study to other stars, such as young Suns, massive stars or evolved RGB stars in order to identify which processes are at the origin of their significantly different dynamics.

I review the development of ideas regarding the angular momentum evolution of solar-type stars, from the early 60's to the most recent years. Magnetic fields are the central agent that dictates the rotational evolution of solar-type stars, both during the pre-main sequence, through star-disk magnetic coupling, and during the main sequence, through magnetized winds. Key theoretical developments as well as important observational results are summarized in this review.

Magnetic fields have been detected at the surface of many stars, where they are responsible for various activity phenomena, and presumably they are present also in their deep interior. They channel stellar winds to large distance, thus increasing the loss of angular momentum. In stably stratified radiation zones, they tend to impose uniform rotation, and may thus interfere with the rotational mixing operating in these regions and influence the evolution of the host star. Moreover, certain magnetic configurations are known to be unstable, and they could produce some mixing of their own. We shall discuss these problems in the light of the latest developments.

The term “magnetosphere” originated historically from early spacecraft measurements of plasma trapped by the magnetic field of earth and other planets. But over the years this concept has also been applied to the magnetically channeled wind outflows from magnetic stars. The review here describes the basic magnetohydrodynamics (MHD) approach used to model such stellar magnetospheres, with emphasis on the central competition between confinement by the magnetic field vs.expansion of the stellar wind outflow. A key result is that, for a star with a dipole surface field B∗, surface radius R∗, and asymptotic wind momentum ${\dot M} v_{\infty}$, this competition can be well characterized by a single “wind magnetic confinement parameter”, $\eta_{\ast} \equiv B_{\ast}^{2} R_{\ast}^{2}/{\dot M} v_{\infty}$. For large η∗, closed magnetic looops can confine parts of the wind up to an Alfvén radius RA ≈ η1/4R∗, leading to “magnetically confined wind shocks” that might produce the relatively hard X-ray emission seen in some magnetic stars. In rotating stars, RA also roughly characterizes the radius up to which material co-rotates with the underlying star. For the outflowing wind, the associated loss of angular momentum, can lead to spindown in the stellar rotation over a time much shorter than the star's evolutionary timescale. For confined material within RA but beyond the star's Keplerian corotation radius RK, the net centrifugal support against gravity can lead to a “rigidly rotating magnetosphere” composed of accumulating trapped wind. This can provide a natural explanation for the rotationally modulated Balmer line emission observed from magnetic Bp stars. Moreover, magnetic reconnection heating from episodic centrifugal breakout events might explain the occasional very hard X-ray flares seen from such stars. Overall, it seems clear that magnetic fields can play a strong role in confining and channeling such stellar wind outflows, providing a natural explanation for various observational signatures structure and variability in the winds and circumstellar envelopes of massive stars.