This course has been taught in the postgraduate programmes at Madrid Autónoma University, Durham University, the University of Valencia (2018), and The Max Planck Institute München (2009). It has also been taught (in different formats) in a number of postgraduate schools: Taller de Altas Energías (TAE 2014, 2015, 2017, 2018, 2019, 2021), 1st International School on Particle Physics and Cosmology (UIMP 2019), Higgs Centre School of Theoretical Physics (2016), STFC HEP School (2015, 2016, 2017).

##### 1.- Introduction

In this session, we present the observational evidence that points towards the existence of dark matter. We introduce the concept of dark matter halo and think about its properties (slides).

##### 2.- Cosmology 101

A brief reminder of Early Universe Cosmology. Emphasis is put on how to compute the abundance of a given species in equilibrium. The Boltzmann equation that describes the evolution of the number density is derived (slides).

##### 3.- Dark Matter Production (Freeze-out)

We apply the Boltzmann equation to the case of a non-relativistic DM particle that “freezes-out”, and define WIMPs (slides).

##### 4.- Dark Matter Production (WIMP models and Freeze-in)

We study some specific particle realisations of WIMPs (concentrating on simplified models) and study special cases, such as resonant annihilation and co-annihilations. We then introduce a new paradigm, where dark matter with very small couplings “freezes-in” (slides).

##### 5- Axions

We review the misalignment mechanism for the production of axions. The cosmological implications are reviewed. We then comment on axion detection.

##### 6- Direct Detection

We show the basics of direct dark matter detection. We derive the equation for the observed detection rate and comment on uncertainties associated to nuclear physics and astrophysical parameters of the dark matter halo (slides).

##### EXERCISES

Exercises for the course (solutions available upon request) (pdf).