Besides a deductive approach to equilibrium statistics and thermodynamics based on one single hypothesis - the form of the microcanonical density matrix - the most important elements of non-equilibrium phenomena are treated. All intermediate steps are completely deducted. Exercises at the end of each chapter help students to deepen their knowledge. In addition to the fundamentals, the text tries to show how large the area of statistical mechanics is and how many applications can be found here. Modern areas such as renormalization group theory, percolation, stochastic equations of motion and their applications in critical dynamics, as well as fundamental thoughts on irreversibility are discussed. The text will be useful for advanced students in physics and other sciences who have profound knowledge of quantum mechanics.