This monograph covers in a unified manner new results on smooth functions on manifolds. A major topic is Morse and Bott functions with a minimal number of singularities on manifolds of dimension greater than five. Sharko computes obstructions to deformation of one Morse function into another on a simply connected manifold. In addition, a method is developed for constructing minimal chain complexes and homotopical systems in the sense of Whitehead. This leads to conditions under which Morse functions on nonsimplyconnected manifolds exist. Sharko also describes new homotopical invariants of manifolds, which are used to substantially improve the Morse inequalities. The conditions guaranteeing the existence of minimal round Morse functions are discussed. Readership Graduate students, postgraduate students, topologists, and algebraists. Reviews "This book is tightly written ... contains a wealth of information on the topological and algebraic apparatus necessary for the construction of minimal Morse functions."  Mathematical Reviews "Clear, concise and readable style ... should prove to be an important contribution."  Bulletin of the London MathematicalSociety "The translation and the printing are faultless."  Zentralblatt MATH Table of Contents  Fréchet manifolds
 Minimal Morse functions on simply connected manifolds
 Stable algebra
 Homotopy of chain complexes
 Morse numbers and minimal Morse functions
 Elements of the homotopy theory of nonsimplyconnected CWcomplexes
 Minimal Morse functions of nonsimplyconnected manifolds
 Minimal round Morse functions
 Bibliography
