Topics on Strings, Branes and Calabi-Yau Compactifications

Basics of some topics on perturbative and non-perturbative string theory are reviewed. After a mathematical survey of the Standard Model of particle physics and GUTs, the bosonic string kinematics for the free case and with interaction is described. The effective action of the bosonic string and the spectrum is also discussed. Five perturbative superstring theories and their spectra is briefly outlined. Calabi-Yau three-fold compactifications of heterotic strings and their relation to some four-dimensional physics are given. T-duality in closed and open strings are surveyed. D-brane definition is provided and some of their properties and applications to brane boxes configurations, in particular to the cube model are discussed. Finally, non-perturbative issues like S-duality, M-theory, F-theory and basics of their non-perturbative Calabi-Yau compactifications are considered.