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A way of construction of semiclassical wave function (SWF) based on theMaslov - Fedoriuk approach is proposed which appears to be appropriate also forsystems with chaotic classical limits. Some classical constructions calledskeletons are considered. The skeletons are generalizations of Arnolds' toriable to gather chaotic dynamics. SWF's are continued by caustic singularitiesin the configuration space rather then in the phase space using complex timemethod. The skeleton formulation provides us with a new algorithm for thesemiclassical approximation method which is applied to construct SWF's as wellas to calculate energy spectra for the circular and rectangular billiards aswell as to construct the simplest SWF's and the respective spectrum for theBunimovich stadium. The scar phenomena are considered and a possibility oftheir description by the skeleton method is discussed.  PACS number(s): 03.65.-w, 03.65.Sq, 02.30.Jr, 02.30.Lt, 02.30.Mv Key Words:Schr\"odinger equation, semiclassical expansion, Lagrange manifolds, classicaltrajectories, chaotic dynamics, quantum chaos, scars

Semiclassical wave functions in billiards built on classical trajectories. Energy quantization, scars and periodic orbits