I. Physical time and the problem of its structure -- I.1 Introduction -- I.2 The order structure of time -- I.3 The topological structure of time -- I.4 The metrical structure of time -- I.5 Conclusion -- Notes -- II. The geometrical nature of physical time: parameter time and coordinate time -- II.1 Introduction -- II.2 Parameter and coordinate -- II.3 Parameter and coordinate time in Newtonian physics -- II.4 Parameter and coordinate time in Einsteinian physics -- II.5 The geometrical nature of time in quantum mechanics -- II.6 Translation of the space and time into the spacetime formalism and vice versa -- II.7 The geometrical nature of time and dynamics -- II.8 Parameter versus coordinate time in the study of time; some philosophical issues -- Notes -- III. Time asymmetry -- III.1 Arrow of time: time asymmetry and time flow -- III.2 Time asymmetry -- III.3 (Ir)reversibility and the time reversal operator T* -- III.4 Time asymmetry and temporal orientability -- Notes -- IV. Thermodynamical time asymmetry and the second law of phenomenological thermodynamics -- IV. 1 Introduction -- IV. 2 The mechanical program -- IV. 3 The thermodynamical program -- IV. 4 Discussion -- Notes -- Epilogue -- Name index.