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We introduce Voevodsky's univalent foundations and univalent mathematics, andexplain how to develop them with the computer system Agda, which is based onMartin-L\"of type theory. Agda allows us to write mathematical definitions,constructions, theorems and proofs, for example in number theory, analysis,group theory, topology, category theory or programming language theory,checking them for logical and mathematical correctness.  Agda is a constructive mathematical system by default, which amounts tosaying that it can also be considered as a programming language formanipulating mathematical objects. But we can assume the axiom of choice or theprinciple of excluded middle for pieces of mathematics that require them, atthe cost of losing the implicit programming-language character of the system.For a fully constructive development of univalent mathematics in Agda, we wouldneed to use its new cubical flavour, and we hope these notes provide a base forresearchers interested in learning cubical type theory and cubical Agda as thenext step.  Compared to most expositions of the subject, we work with explicit universelevels.

Introduction to Univalent Foundations of Mathematics with Agda