Scattering resonances replace bound states/eigenvalues for spectral problems in which escape (scattering) to infinity is possible. These states have rates of oscillation and decay and that information is elegantly encoded in considering the corresponding ``eigenvalues" as poles of the meromorphic continuation of Green functions. The most famous ``pure maths" example is given by zeros of the Riemann zeta function which can be interpreted as resonances for scattering on the modular surface. In ``applied maths" they appear anywhere from gravitational waves to MEMS (Micro-Electro-Mechanical Systems). The mini course will provide a gentle introduction in the setting of potential scattering in dimension three. Only basic functional analysis will be a prerequisite. 1. One dimensional scattering: intuition behind outgoing and incoming waves and the definition of scattering resonances. 2. Analytic Fredholm theory and, as application, meromorphic continuation of Green's function for potentials scattering in dimension three. 3. Resonance free regions and expansion of waves in terms of resonances. 4. Counting resonances: upper bounds and existence (and some open problems). Complex valued potentials with no resonances. Section 2 of https://math.berkeley.edu/~zworski/revres.pdf (Bull Math Sci '17) will provide a reference with a more detailed presentation in the forthcoming book http://math.mit.edu/~dyatlov/res/ (AMS '19, to appear).