  In these notes the main theoretical concepts and techniques in the field of
mean-field spin-glasses are reviewed in a compact and pedagogical way, for the
benefit of the graduate and undergraduate student. One particular spin-glass
model is analyzed (the p-spin spherical model) by using three different
approaches. Thermodynamics, covering pure states, overlaps, overlap
distribution, replica symmetry breaking, and the static transition. Dynamics,
covering the generating functional method, generalized Langevin equation,
equations for the correlation and the response, the Mode Coupling
approximation, and the dynamical transition. And finally complexity, covering
the mean-field (TAP) free energy, metastable states, entropy crisis, threshold
energy, and saddles. Particular attention has been paid on the mutual
consistency of the results obtained from the different methods.
