  This is a non-standard exposition of the main notions of quantum mechanics
and quantum field theory including some recent results.
  It is based on the algebraic approach where the starting point is a
star-algebra and on the geometric approach where the starting point is a convex
set of states.
  Standard formulas for quantum probabilities are derived from decoherence.
This derivation allows us to go beyond quantum theory in the geometric
approach. Particles are defined as elementary excitations of the ground state
(and quasiparticles as elementary excitations of any translation invariant
state).
  The conventional scattering matrix does not work for quasiparticles (and even
for particles if the theory does not have particle interpretation). The
analysis of scattering in these cases is based on the
  notion of inclusive scattering matrix, closely related to inclusive
cross-sections. It is proven that the conventional scattering matrix can be
expressed in terms of Green functions (LSZ formula) and the inclusive
scattering matrix can be expressed in terms of generalized Green functions that
appear in the Keldysh formalism of non-equilibrium statistical physics.
  The derivation of the expression of the evolution operator and other physical
quantities in terms of functional integrals is based on the notion of the
symbol of an operator; these arguments can be applied also in the geometric
approach.
  The notion of inclusive scattering matrix makes sense in the geometric
approach (but it seems that one cannot give a definition of the conventional
scattering matrix in this situation).
  The geometric approach is used to show that quantum mechanics and its
generalizations can be considered as classical theories where our devices can
measure only a part of observables.
