Title: Two Higgs Doublet Model and Some Fantasies About the History of Time Abstract: The Two Higgs Doublet Model (2HDM), the simplest extension of the Standard Model, provides an explanation for the Electroweak Symmetry Breaking (ESB). We use the invariance of physical picture under a change of Lagrangian, the reparametrization invariance in the space of Lagrangians and a particular case of the latter -- the rephrasing invariance, to analyse the properties of the 2HDM. We find that some parameters of the Lagrangian such as tan(beta), are reparametrization-dependent and therefore cannot be fundamental. We use the Z_2-symmetry of the Lagrangian, which prevents $phi_1 <---> phi_2$ transitions, and different levels of its violation, soft and hard, to describe the physical content of the model. In general, the broken $Z_2$-symmetry allows for a CP violation in the physical Higgs sector. We argue that the 2HDM with soft breaking of the $Z_2$-symmetry is a natural model in the description of the ESB. Depending on the parameters of the Lagrangian, the minimization of Higgs potential in the 2HDM gives two different vacuum states: - the standard vacuum, describing our world, and charged vacuum with massive photon. Naturally, we work with the standard vacuum and find a simple necessary and sufficient condition for CP violation in Higgs sector. The interaction of Higgs fields describing the ESB with the fields responsible for inflation in early Universe can be responsible for a very interesting set of phenomena that have probably taken place after the Big Bang.