Most content on the matter tend to involve a lot of formalism - the most popular one being What's algebraic about Algebraic Effects. This document compiles a list with some pointers to help with the navigation.
Pre-requisites: Haskell, Monads, Monad Transformers
This article takes a hands on approach to illustrating Algebraic Effects as means to provide purity without introducing Monads all over. Employing monads to model effectful computations often require monad transformers so that different monads can be composed together. Algebraic Effects, unlike monads, are inherently compositional and provide an interesting alternative to managing side effects.
Pre-requisites: Javascript
Javascript does not have Algebraic Effects. In this article, Dan Abramov provides intuition for what Algebraic Effects are - using resumable exceptions as the mental model to understand how Algebraic Effects work - and the implications to possibilities of abstractions that open up. This article does not talk about types or purity of effectful computations. Includes links to more resources to help learn Alg. Effects.
Pre-requisites: OCaml
The multicore team at OCamllabs uses algebraic effects (untyped) as basic primitive to manage thread scheduling in the compiler. In this tutorial, KC Sivaramakrishnan (and others) provide step by step explanation of using Alg. Effects as resumable exceptions that reduce monad poisoning in concurrent OCaml code and also how popular language constructs like async/await, generators/iterators, message passing, exception handling etc can all be expressed with Algebraic Effects and handlers.
Pre-requisites: Abstract Algebra (and some Category theory)
In this series, Andrej Bauer explains algebraic nature of Algebraic Effects. The first lecture assumes the audience understands basic Abstract Algebra and is comfortable with some mathematical rigour involved in understanding them. Explaining the basics of Universal Algebra (signatures, equations, models, co-models etc), it explains what makes Alg. Effects algebraic in nature.
Eff is an experimental programming language that acts as a playground of research ideas around Algebraic Effects. This tutorial introduces what it means for a programming language (not necessarily Eff) to model it's effectful operations as effectful computations and handlers. This tutorial is aim more at those who dont shy away from operational/denotational semantics of a hypothetical programming languages.