The aim of this minicourse is to introduce fundamental concepts in hyperbolic geometry, such as limit sets, geometric finiteness, and critical exponent, and Mostow rigidity. We will discuss examples of arithmetic hyperbolic manifolds, and illustrate flexible geometric constructions like Dehn filling, quasi-conformal deformation, and the gluing constructions of non-arithmetic lattices by Gromov and Piatetski-Shapiro.