For understanding the Austria that shaped modern Europe, start with Stefan Zweig's The World of Yesterday, a memoir of Vienna's golden age before the wars destroyed it — it's elegiac, personal, and devastating. Simon Winder's Danubia is the best modern history of the Habsburg Empire: irreverent, funny, and genuinely illuminating about why Central Europe looks and feels the way it does. Andrew Wheatcroft's The Habsburgs covers the dynasty in more scholarly depth. Viktor Frankl's Man's Search for Meaning, written by a Viennese psychiatrist who survived the concentration camps, transcends its Austrian origins but is inseparable from them.
Austrian literature has a dark, sharp edge. Thomas Bernhard, the country's great literary provocateur, wrote furious novels about Austrian hypocrisy and provincial suffocation — Woodcutters and Wittgenstein's Nephew are good starting points. Robert Musil's The Man Without Qualities, set in the final years of the empire, is one of the great unfinished novels in any language — ambitious, ironic, and very Viennese. Elfriede Jelinek, the Nobel laureate, writes with savage intensity about power, gender, and Austrian society; The Piano Teacher is her most accessible work. For something lighter, try Daniel Kehlmann's Measuring the World, a witty novel about Humboldt and Gauss that was a massive bestseller in the German-speaking world.
If you want practical reading, the Lonely Planet and Rough Guide Austria editions are both solid. For walking and hiking, the Rother Walking Guides cover Austrian regions trail by trail with detailed route descriptions. And if you're interested in Viennese music, Alex Ross's The Rest Is Noise gives superb context for the city's role in the history of classical music, from Mahler through the Second Viennese School and beyond.