Introduction

String theory is by now, beyond the Standard Model (SM) of particle physics, the best and most sensible understanding of all of the basic components of matter and their interactions in an unified scheme. There are well known the `aesthetic' problems arising in the standard model of particles, they include the hierarchy problem, the abundance of free parameters and the apparent arbitrariness of the flavor and gauge groups. The SM is for this reason commonly regarded as the low energy effective description of a more fundamental theory, which solves these problems (for a nice review see [1]). It is also widely recognized that Quantum Mechanics and General Relativity cannot be reconciliated in the context of a perturbative quantum field theory of point particles. Hence the nonrenormalizability of the general relativity can be regarded (similarly to the standard model case) as a genuine evidence that it is just an effective field theory and new physics associated to some fast degrees of freedom should exist at higher energies (for a review, see for instance [2]). String theory propose that these fast degrees of freedom are precisely the strings at the perturbative level and at the non-perturbative level the relevant degrees of freedom are higher-dimensional extended objects called D-branes (dual degrees of freedom). At the perturbative level String Theory has intriguing generic predictions such as: $(i)$ Spacetime supersymmetry, $(ii)$ General Relativity and $(iii)$ Yang-Mills fields. These subjects interesting by themselves are deeply interconnected in a rich way in string theory. The study of theories involving D-branes is just in the starting stage and many surprises surely are coming up. Thus we are still at an exploratory stage of the whole structure of the string theory. Therefore the theory is far to be completed and we cannot give yet concrete physical predictions to make contact with collider experiments and/or astrophysical observations. However many aspects of theoretic character, necessary in order to make of string theory a physical theory, are quickly in progress. The purpose of these lectures is to overview the basic ideas to understand these progresses. We don't intend to be exhaustive and we will limit ourselves to describe the basics of string theory and some particular few new developments like Calabi-Yau compactifications of the M and F theories. We apologize for omiting numerous original references and we prefer to cite review articles and some few seminal papers. We first survey the the bosonic and superstring theories, including Calabi-Yau compactifications from the perturbative point of view. T-duality and $D$-brane theory are also considered. After that, we devote some time to describe the string dualities and the web of string theories connected by dualities. M and F theories are also briefly described. Finally we overview an approach to non-perturbative Calabi-Yau compactifications of M and F theories. truecm