These notes are designed as a text book for a course on the Modern Physics Theory for undergraduate students. The purpose is providing a rigorous and self-contained presentation of the simplest theoretical framework using elementary mathematical tools. A number of examples of relevant applications and an appropriate list of exercises and answered questions are also given.

The first part is devoted to Special Relativity, concerning in particular space-time relativity and relativistic kinematics.

The second part deals with Schroedinger's formulation of quantum mechanics. The presentation concerns mainly one dimensional problems, in particular tunnel effect, discrete energy levels and band spectra. The three dimensional Schroedinger equation is discussed in the case of a cubic box and in that of central potentials; in particular we give some details on the harmonic oscillator, the spherical box and the Coulomb potential.

The third part concerns the application of Gibbs statistical methods to quantum systems and in particular to Bose and Fermi gasses.