This is one of the most useful books for anyone exploring the Wake. By giving an abridged and usually plain-language version, it is at least a starting point. The critics' quibble is principally with the introductory statements and the footnotes which tend to interpret the Wake in terms of myth. Such interpretations are not wrong: they are just one of many valid ones. This is one of the four books you must have.

Geared to the Wake page by page, McHugh gives some of the literary and historical allusions, meanings of strange words, and some cross references gleaned from a variety of sources. It takes a little effort to learn how to use this book with ease, but it's worth it: it is vital to study of the Wake.

This is almost a paragraph-by-paragraph study, pointing out allusions, themes, and relevant biographical information. Although written in a breezy idiosyncratic way, it's packed with useful information.

A much more detailed examination of the literary sources Joyce used in the Wake than the previously listed books, this augments them.

Interesting for its coverage of extra-Wake material such as Joyce's notebooks, various scholarly works and the reading group experience, this volume should be read principally for the detailed analyses of two sections of the Wake.

Adaline Glasheen
Third Census of Finnegans Wake
University of California Press 1977

This is an exhaustive list of Wake personnages, fictional and real, with short descriptions and cross references.

Although it covers all of Joyce, it includes a great deal of useful Wake material both for the tyro and the advanced Wakean. Both this and Glasheen have valuable summaries of each chapter of the Wake.
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Although this might appear to be a tool only for advanced scholars of the Wake, it can clarify the text for all readers. Since Joyce, in reworking the initial draft, augmented and obscurified it, this first draft often has clearer uncoded versions which can be used to fathom the final text.

The sections on the Wake give an excellent overview.