This text brings together a number of lectures given between 1993 and 1999 as part of a series hosted by the Federal University of Pernambuco, in which internationally established researchers lectured in Recife, Brazil, on classical or celestial mechanics. The material presented includes a balance of pure and applied research and of complete and incomplete results. The contributors to this volume are Dieter Schmidt, Ernesto Perez-Chavela, Mark Levi, Placido Taboas, Jack Hale, Jair Koiller, Hildeberto Cabral, Florin Diacu and Alain Albouy. The topics covered include central configurations and relative equilibria for the N-body problem, singularities of the N-body problem, the two-body problem, normal forms of Hamiltonian systems and stability of equilibria, applications to celestial mechanics of Poincare's compactification, the motion of the moon, geometrical methods in mechanics, momentum maps and geometric phases, holonomy for gyrostats, microswimming and bifurcation from families of periodic solutions.