This was a large-format (approximately A4) softcover book; I don't recall the cover art. It was given to me as a gift by my aunt, so it may have been picked up remaindered and actually date from earlier.
The book was framed as a series of lectures, exercises and tests for Earth recruits who were fighting some aggressive evil empire. I don't remember if they were mind-controlled humans, robots, or generic aliens. The enemy had some Sauron-type figure (dictator, but also the most powerful of them and possibly superhuman) driving them. There were story-like elements in addition to expositional blobs and diagrams, but still an advancing story; by the end of the book the reader is on the Earth flagship fighting the enemy flagship.
Some of the story pieces were slice-of-life descriptions, but I think there may have been a few rescue/adventure pieces like an old-style planetary romance. I may be confusing this with other works, but I wouldn't be surprised if there were an older scientist type and a plucky action girl as supporting characters.
One set of puzzles I recall was "identify this object in zero G" where you were shown an unusual perspective on a common item and asked to identify it; the one I recall most strongly was a point-on view of needle-nose pliers. Another of the puzzles presented a blank field (supposed to be the blackness of space, but not inked to black) scattered with navigation lights, and the reader was asked to determine what ships were present and the likely scenario in progress. Most of these were single-person, but some could be competitive.
The final battle against the enemy was constructed as a 2-player game with alternating turns of blind shot-taking, something like the game Battleship, except that after each shot you found out how much you missed by, and then the other player's ship moved. (Basically after 3 or 4 shots you each knew roughly where your enemy was, and you were chasing one another around, trying to be the first to correctly guess which way the other would move.)
Thinking some more about the game, it was played on a grid, with the ships located at the intersections. When you fired you specified a point, and the targeted player counted how many points away the shot hit (Manhattan metric; x + y) did some pointless calculation involving a spinning disc thing set into the cover of the book and gave the result to the firing player. The firing player reversed the calculation (hence pointless) to get the distance, and plotted the cloud of possible points. Then the targeted player moved along one of the edges to an adjacent point.
So the book had some kind of circular wheel built into the front or back cover.
In terms of art, I recall the human ships being roughly doughnut-shaped or maybe something vaguely like a turtle, while the enemy were far more sleek and wedge-shaped. (Maybe kind of a Star Destroyer look?)