Old Irish, old-school
This book drops the learner right in at the deep-end of Old Irish. It takes a single story, and deconstructs it word by word, across many chapters. If you ever took Latin or Ancient Greek (as I did), you'll be familiar with this approach, which is quite different from that used in learning modern languages: after all, you will never need to ask "When does the bus leave?" or "Can I have the check please?" in those languages. So instead, you read what Caesar wrote about the wars with the Gauls, and by breaking it down word by word, learn the grammar, almost by osmosis.
Like reviewers I have read elsewhere, I didn't find this approach terribly helpful. There are lots of little tidbits, but little in the way of overall structure. In one chapter, you learn the accusative of a few masculine nouns (those occurring in the text), in another the genitive of feminine singular - after a few, your brain is crying out for some formal structure (e.g., "In this chapter, we will learn about the use of the genitive case").
Still, each chapter does contain informative paragraphs on grammar and culture. I especially enjoyed those which helped fit Old Irish into the historical Indo-european context, and since this is one of the primary reasons to be interested in Old Irish, perhaps the authors wrote more engagingly about those aspects than others.
Some day, I would love to see a book that compares the differences between Old and Modern Irish - many of the grammatical aspects of Old Irish that seem particularly foreign to non-Irish speakers, are in common usage in Modern Irish, and so merit little discussion. To me, as someone with near-fluent Irish, the really interesting stuff is what's different between the Old and the New, but clearly that market is very tiny.
This book is slight, and if you're comfortable with the archaic presentational style, you might find it useful. I can't imagine that one would really attain an understanding of grammar, but at least one might understand the story which forms the backbone of all the lessons, and thereby gain insight into the culture and mindset of Old Irish culture.