The given book presents an introduction to the basic concepts and mathematical tools of quantum mechanics. It is based on the material that I have been using in teaching the first course on quantum mechanics to the undergraduate and M.Sc. students at I. I. T. Delhi. The last chapter on relativistic generalization of quantum mechanics does not constitute a part of the usual course and has been added for those who wish to have some basic ideas of relativistic quantum mechanics.

In presenting the material, I have taken into account the feedback of the students about the conceptual as well as the mathematical difficulties faced by them during the course. As a result, I have tried to be as simple as possible. Therefore, I might appear to be too simple and repetitive at times and I hope the knowledgeable reader will pardon me for that.

The book starts with the basics of quantum mechanics in the traditional way by using the fundamental tools of mathematical analysis with an emphasis on the physical explanation for the mathematical treatment of the topics. This part includes the introduction to the concept of the state of a quantum mechanical system, operators and their algebra, the basic postulates of quantum mechanics and the solution of the Schrödinger equation for important one-dimensional systems. The algebraic formalism in the traditional language of Dirac is then introduced and the entire earlier material is reformulated in this language so as to make the reader comfortable with the modern language of quantum mechanics. In the later chapters of the book, I deal with the three-dimensional problems, hydrogen atom, quantum mechanical theory of orbital as well as spin angular momentum, and many particle systems. Simple effects related to the quantum mechanical treatment of the motion of a charged particle in the presence of a magnetic field are also presented. The basic concepts related to the symmetries of a system and the corresponding laws of conservation are then introduced and developed. In particular, the relationship between the fundamental quantum mechanical operators and the generators of the continuous groups of symmetries of spacetime are established and discussed. The book ends with an introduction to relativistic quantum mechanics.