Kazakhstan is a big country with a population dispersed over more than 20 cities with over 100.000 inhabitants. If you have to move around quickly, you will be happy to find out there are many domestic flights. Almaty airport and Astana airport are now reasonably well-connected with Europe, Asia and the Middle East, with a minor role for Shymkent and Aqtau as international airports.
Inside Kazakhstan, 5 companies provide domestic flights: Air Astana, SCAT, Qazaq Air, Irtysh Air and Bek Air. Be sure to book Astana – Almaty flights in advance, they sell out quickly. Especially weekends and holidays are popular moments to escape the capital.