This book is devoted to present a unifying geometric framework for Mechanics and Classical Field Theory, as it has been developed by us in collaboration with the group of Mathematical Physics in Torino, as well as other groups spread all over the World. The explicit aim is to show that there is a single unifying geometrical language for all Physics of fundamental interactions, a unifying language which allows one to treat on equal footing all structural issues of Lagrangian field theories, from field equations to symmetries and conservation laws. This language is the language of gauge natural bundles, a piece of Mathematics which has been developed fairly recently (see [KMS93]). We shall show that exactly this language allows to discuss at once all known classical Field Theories, including General Relativity, Gauge Theories, their mutual interactions, all kinds of Bosonic and Fermionic matter, both in standard Physics and in their supersymmetric versions.