I am taking this from a website cited at the bottom. Popsci has a LOT of cool beer articles. Fractional freezing is the best way to increase the alcohol content of beer.
Fractional freezing -- "jacking" in old parlance -- has a long history in the United States. The beverage applejack was produced using this method by first fermenting apple juice into hard apple cider. Then barrels of this cider were left outside during the winter and the connoisseur would occasionally fish out the frozen chunks of water, leaving an ever-concentrated batch of hard alcohol behind. At some point in the 20-25 percent ABV range, the liquor would stop freezing at ambient temperatures and the booze was ready to consume as "Jersey Lightning." It was also used as currency.
Moving into the malt-beverage world, brewers in Germany use fractional freezing to make eisbock. These brews are usually just regular bock beers, which clock in at 6 percent ABV, freeze-concentrated to something in the 13 percent ABV range. Frankly, there are probably easier ways to get high-proof beers (make a barleywine, for example) than by starting with a mid-strength one and concentrating it, but there's a market for eisbocks and it's possible to find them in the US as well. A more infamous set of freeze-concentrated beers was made by the Scottish brewery BrewDog in their quest to make "the strongest beer in the world." The first was Tactical Nuclear Penguin, a beer that started with an ABV in the teens and ended at 32 percent ABV. Then a little brewing war started up between BrewDog and German brewery Schorschbräu to make ever-stronger beers. Schorschbräu made a Schorschbock at 40 percent ABV, BrewDog countered with Sink the Bismarck at 41 percent ABV. Then came another beer at 55 percent ABV (that's 110 proof, my friends). Schorschbräu is current record-holder with Schorschbock 57, at 57 percent ABV.