The Album is your collection of puzzles. Its front page lists the four kinds, Square, Square X, Irregular, and Irregular X; choose one, then a difficulty, to see those games. Each saved game shows a picture of your progress, pencil marks included, and a badge counting the cells still to solve, or a gold check once it is solved. A puzzle you imported also carries a small mark for where it came from.
The pictures always show each game as it is. The picture of the game you have open follows your moves, and so does any smaller picture of it on the front page or on the list of difficulties for its kind.
Tap the back arrow or the list icon on the game screen to return to the album. Your game is automatically saved.
On a difficulty's page of games, or in its slideshow, tap the + button in the title bar to add a new puzzle there, drawn from a pre-generated queue for an instant start. The new game comes into view, but you stay in the album. With Manual game generation on in Settings, you choose the kind and difficulty yourself, and a game of another kind or difficulty goes to its own page.
Tap a saved game to see it in the slideshow, one game at a time at full size. Swipe left and right to browse your games, then tap to play. Long-press a game in the album to delete it.
To bring in a puzzle from somewhere else, or to share one, see Importing & Sharing.
Split view. On a tablet, or in a large window on a computer or in a browser, the album and the game sit side by side; see Split view and Slideshow in Settings. In split view the game has no back arrow or list icon, because the album is already beside it: to play another game, pick it in the album, and the game you leave is saved as you switch. Turning split view on or off, or resizing the window, keeps your place in the album and the game you have open.
On the web, the album lives in your browser's storage. The browser keeps it for a while but may clear it. The installed app keeps games as files on your device.