I have been testing out the Forward Chess app over the last few weeks and I have to say right away that I like what I see. It's a free app, and it can be found on Google Play and the Mac app store. Android, iPad and iPhone are all compatible.
Essentially, the app is a reader for chess books. The books can be purchased from the stores mentioned above and they download to the relevant device in a matter of seconds. Once downloaded, the books are very easy to locate and access.
The table of contents in each book is linked to the relevant sections of text, so a simple click takes the reader to the exact part one would like to study. When playing through a game, all of the moves are active too, so touching one will automatically summon a chessboard onto the top of the screen. A reader can then try out moves on the board and analyse accordingly. The board can be flipped instantly (for example, to study form the point of view of the black pieces) and moves can be skipped by pressing on a later piece of notation. The on-screen board will immediately catch up with the action.
In addition to those features, the Stockfish 4 engine can summoned instantly, allowing in-depth analysis of any given position. It may be useful (and occasionally entertaining) to compare the authors' lines of analysis with those of the all-seeing engine.
The controls are kept as simple as possible, making the learning phase as simple and intuitive as possible.
Six chess publishers are working in partnership with Forward Chess, namely: Mongoose Press, New in Chess, Quality Chess, Chess Stars, Russell Enterprises and Chess Informant. The number of books being made available is increasing all of the time. Some of the more recent titles come out simultaneously via the app and in printed form.
The list of books currently available can be found here and general details about the app can be found on the Forward Chess website. There's even a forum, on which to discuss the app and forthcoming titles.
Downloading the app automatically gives a couple of sample books to try: On Life and Chess by Sergey Shipov and True Lies by Lluis Comas Fabrego. Some of the books in the store offer sample chapters too, which can downloaded for free.
I am enjoying using the app and strongly advise you to give it a try.