  These lectures, presented at the 2022 TASI summer school, give an
introductory overview of first-order phase transitions in the early Universe,
baryogenesis, and the resulting gravitational wave phenomenology. We introduce
thermal field theory via the imaginary time formalism, and comment on the
pitfalls of 1-loop calculations and alternative approaches. Then, we discuss
how to calculate the false vacuum decay rate in first order phase transitions,
of which we give various examples in theories beyond the Standard Model.
Baryogenesis is presented via the Sakharov conditions, and how they are met in
important classes of examples. Finally, we explore gravitational waves from the
early Universe, first reviewing the basics of gravitational wave generation and
then focusing on the specific example of first order phase transitions.
