The main topics covered in this text, which contains the proceedings of a NATO ASI conference held in Montreal, are: non-smooth critical point theory; second order differential equations on manifolds and forced oscillations; topological approach to differential inclusions; periodicity of singularly perturbed delay equations; existence, multiplicity and bifurcation of solutions of nonlinear boundary value problems; some applications of the topological degree to stability theory; bifurcation problems for semilinear elliptic equations; ordinary differential equations in Banach spaces; and the centre manifold technique and complex dynamics of reaction diffusion equations.