This book is an introduction to modern methods of symplectic topology. It is devoted to
explaining the solution of an important problem originating from classical mechanics: the
'Arnold conjecture' which asserts that the number of 1-periodic trajectories of a
non-degenerate Hamiltonian system is bounded below by the dimension of the homology of the
underlying manifold. The first part is a thorough introduction to Morse theory a fundamental
tool of differential topology. It defines the Morse complex and the Morse homology and
develops some of their applications. Morse homology also serves a simple model for Floer
homology which is covered in the second part. Floer homology is an infinite-dimensional
analogue of Morse homology. Its involvement has been crucial in the recent achievements in
symplectic geometry and in particular in the proof of the Arnold conjecture. The building
blocks of Floer homology are more intricate and imply the use of more sophisticated analytical
methods all of which are explained in this second part. The three appendices present a few
prerequisites in differential geometry algebraic topology and analysis. The book originated in
a graduate course given at Strasbourg University and contains a large range of figures and
exercises. Morse Theory and Floer Homology will be particularly helpful for graduate and
postgraduate students.
