David Mamet, the playwright, film-maker, polemicist and now blogger, once described his trademark close crop as “the haircut of an honest, two pair of jeans working man - a man from Chicago, a man without vanity whose being stands without need of either introduction or apology”. Nonetheless, Mamet gets an introduction, and a generous apprai-sal, if not an apology, in Ira Nadel's David Mamet: A Life in the Theatre (Methuen, £25/offer £22.50), which has a go at probing the Mamet enigma. That enigma deepened recently when Mamet publicly rejected his “brain-dead liberal” past and revealed his inner conservative, finding that big government was bad and Bush no worse than Kennedy. Perhaps we shouldn't have been surprised. Mamet collects guns and knives and his plays have made a speciality of aggressively individualist male jousting. But we thought that was a critique: now it seems more of a love affair. Enigma indeed.

Shakespeare was another enigma. If he was Shakespeare, that is. Jonathan Bate, at least, is satisfied that the plays attributed to him were written by the man from Stratford-upon-Avon, and in Soul of the Age (Penguin Viking, £25/£22.50) brilliantly makes use of what scant documentary evidence exists to build up a picture of “the life, mind and world” of our national genius. Combining acute readings of the works with a profound sense for the history of the period, he tells us about Shakespeare's class sensitivities, county loyalties in Elizabethan England, how an education in Latin verse fed into Shakespeare's writing, his expertise in botany ... and much more. Fascinating, all of it.

Also weirdly compelling is Martin C. Strong's Lights, Camera, Soundtracks (Canongate, £25/£22.50), a volume in the tradition of those heroic souls who spend years building models of ocean liners out of matchsticks. Strong's labour has been to preside over a 900-page guide to popular music in the movies. It took six years. His work rate of 70 hours a week increased near the end to 100 (I calculate that there are only 112 one could possibly devote to working). His laptop broke down. And yet here is his Queen Mary - safely escorted from potting shed to publisher. The structure is a little confusing, but once mastered you will find exhaustive documentation on Woodstock, Hysteria: the Def Leppard Story, Uncle Meat, Shaft, and thousands of other cases where the worlds of pop music and film more or less fruitfully collided.

A cartoon in Private Eye is entitled Scenes You Seldom See. One candidate could be the repentant critic. Perhaps direct self-contradiction is the nearest thing we'll get. Thus David Thomson, in a 1996 hatchet job, Rosebud, opined of Orson Welles's Chimes at Midnight that “the bogusness of the man and actor was glaring”. The film was “too sentimental” and the landscapes “inappropriate”. In the 2008 Have You Seen ...? (Allen Lane, £22/£19.80) Thomson finds the film a “masterpiece” in which “sentimentality is crushed at every turn”. The locations are “not quite England - but who cares?” It is good to have Thomson back in the land of reason. For despite his periodic venom, his writing always glows with passion. And in the 1,000 films he dissects here he enrages, exasperates, but never leaves one indifferent.

Another seasoned film writer, Richard Schickel, teams with George Perry to supply the words for You Must Remember This (Running Press, £29.99/£26.99), a glossy resumé of Warner Bros' 100-odd years in the movie business. It's been quite a journey - from the silent canine star Rin-Tin-Tin through The Jazz Singer, Busby Berkeley, Cagney, Bogart, Casablanca, James Dean, Looney Tunes, Kubrick, Eastwood, to Batman and Harry Potter. Schickel is too wily a commentator to make it merely a bland puff piece, and the pics are outstanding.

Dirk Bogarde could be a little on the waspish side, and early on one fears that his letters, collected in Ever, Dirk (Weidenfeld & Nicolson, £25/£22.50), will descend into naked bitchery, as Anthony Quinn, Alan Bates, Richard Burton, Stanley Baker, Michael Redgrave, etc, all get the rough edge of his typewriter ribbon. But Bogarde was funny and wise too, and capable of great affection and kindness - when the right buttons were pressed. His judgments on his own films were often inaccurately optimistic, but on people he was generally spot on.

Actors preparing for the stage are the subject of Simon Annand's photographs in The Half (Faber & Faber, £30/£27). The images are stunning, in revealing black and white, but if you hope to find a record of thespians caught off guard, forget it. Ralph Fiennes may be shaving, Maureen Lipman standing on her head and Saffron Burrows bathing her feet, while numerous others pull on a last-gasp cigarette, but they are already in another place, no longer merely themselves. Perhaps actors are only really natural when they're acting.

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