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I've read most of Grätzer's Universal Algebra and have completed it with most of S. Burris and H.P. Sankappanavar's A Course in Universal Algebra.

I want to dive a bit deeper than these introductions into universal algebra and I'm currently looking for references.

I've seen in another question similar to this one a reference to C.Bergman's Universal Algebra : Fundamentals and selected topics but I'm not sure it goes much further than the previously mentioned books.

So I'm interested in the geometric (universal algebraic geometry) and categorical aspects of universal algebra, but also in universal algebra in general. So if you could provide references that go in this direction, I'd be glad to see them.

Maxime Ramzi
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One subject which played a particularly important role is commutator theory, and in particular tame commutator theory, mainly (if my understanding is correct) due to McKenzie and Hobby; there are a number of sources on this topic, including this paper by Kiss on the tame theory and this book by Freese and McKenzie on the general theory for congruence-modular varieties. Freese and McKenzie's book is self-contained but goes rather quickly, so may be ideal for you if you're interested in this particular direction.

This survey article by Willard may also be of interest, as it mentions a number of other more specialized areas and advanced sources. In particular, section 5 discusses tame congruence theory.

Noah Schweber
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This book deals well with the categorical view of universal algebra.

Guilherme Gondin
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  • Also I've made a survey of universal algebra, if you find any good refferences post there, it's community wiki: https://mathoverflow.net/questions/337963/a-survey-on-universal-algebra?noredirect=1#comment845334_337963 – Guilherme Gondin Dec 25 '19 at 00:28