This chapter explores stable, finite-energy solutions to non-linear classical field theories known as topological objects. It begins with an analysis of the sine-Gordon model, which features kink and anti-kink solitonic solutions associated with a conserved winding number. The discussion then moves to two-dimensional systems, demonstrating that coupling a complex scalar field to an abelian gauge field is necessary to achieve finite-energy vortex line solutions, such as the Abrikosov flux lines found in type II superconductors (Higgs model). Finally, the chapter examines topological solutions in Yang-Mills theory, establishing that static, finite-energy solutions exist only in four spatial dimensions. This leads to the detailed study of the instanton solution, the associated Chern-Simons current, and the Potryagin topological index, which quantifies the winding number and describes tunneling between degenerate vacuum states.