You can't book directly through ITA Matrix -- but you can use it to zero in on your dream ticket, then head to that airline's site or hand things over to a travel agent (the site gives you the booking and fare codes that agents need to find the same deal).
BootsnAll Launches Indie – the World’s First Multi-Country Flight Finder
Dohop is a flight finder based in Reykjavik—similar to sites like Orbitz or Expedia—but much more user-friendly in my opinion. Because of an awesome algorithm and business strategy, Dohop always seems to find the best deals for flights, hotels, and car rentals on the market—its resources include over 1,200 airlines and travel agencies. Here are some reasons you should book your next flight with Dohop!