  These lecture notes are based on the second course in a series of lectures at
the Spring school "Non-archimedean geometry and Eigenvarieties" in March 2023
in Heidelberg. The objective of the first three courses was to give an
introduction to the theory of adic spaces. Building up on the theory of Huber
pairs presented in John Bergdall's lecture we explain the construction of adic
spaces. We study some important classes of adic spaces such as rigid analytic
spaces and formal schemes and show the connections between them. In the course
of the lecture we will illustrate the respective concepts with the fundamental
examples of the open and closed disc and the affine line.
