  We provide an introduction to logarithmic potential theory in the complex
plane that particularly emphasizes its usefulness in the theory of polynomial
and rational approximation. The reader is invited to explore the notions of
Fekete points, logarithmic capacity, and Chebyshev constant through a variety
of examples and exercises. Many of the fundamental theorems of potential
theory, such as Frostman's theorem, the Riesz Decomposition Theorem, the
Principle of Domination, etc., are given along with essential ideas for their
proofs. Equilibrium measures and potentials and their connections with Green
functions and conformal mappings are presented. Moreover, we discuss extensions
of the classical potential theoretic results to the case when an external field
is present.
