Many visitors to Kazakhstan have just a few days to spare but, thanks to the concentration of sites in and around Almaty, and the reasonable provision of domestic flights, this shouldn't prevent you from seeing something of the country.
Starting in Almaty, a weekend is ample time to visit the city's Panfilov Park and wooden Holy Ascension Cathedral before spending the afternoon getting to know the locals (and doing some all-important souvenir shopping) at Green Bazaar or taking the waters at the Arasan Baths. Spend the evening watching a performance at the Abai Opera and Ballet Theatre before having a nightcap at one of the city's numerous pubs and bars. Rise early the next morning and go to Republic Square and The Independence Monument. Choose between the Central State Museum and the often overlooked Museum of Folk Musical Instruments of Kazakhstan for a strong introduction to Kazakhstan's past and culture. In the late afternoon take the cable car from the city centre to Kok-Tobe, making sure you get your photo taken with The Beatles, and enjoy a drink while you watch the sunset over Almaty.
If you are in Kazakhstan for a week, start with a few days in Almaty before heading out into the spectacular Ile Alatau National Park. If it's winter and you're a ski bunny, you'll probably get no further than Chimbulak and Medeu, but hikers should continue a little further to the Aksai Gorge and the unprepossessing village of Ungirtas, which some believe is the hub of the universe. Tamgaly, west of Almaty, is home to the most impressive collection of petroglyphs (ancient rock carvings) in Kazakhstan. There are over 4,000 examples dating from the Bronze Age to the present, and it is well worth spending a full day at this UNESCO World Heritage Site.
Two weeks will allow you to travel further afield without relying on flights. From Almaty travel west to the spectacular Aksu Canyon where the white-water Aksu River has carved 600m-deep channels up to 500m wide through the rock. You can travel by 4x4 or on foot and are guaranteed to see a wide variety of flora and bird life. Shymkent is famous only for its lead smelter and oil refinery, but it makes a convenient stopover point for Sayram, an ancient oasis inhabited by Nestorians and later overrun by Muslim forces and then again by Genghis Khan. Sections of the fortified walls remain, as do several mausoleums and the 15m-high Hisr Paygambar Minaret. Travelling north, stop at the tomb of Islamic mystic Arystan Bab before reaching the more famous site in Turkestan, where Bab's disciple Khodja Ahmed Yassaui is interred. His mausoleum is the finest work of Timurid architecture in Kazakhstan, and the neighbouring tombs and mosques have also been well restored. If you have the time and money to afford a permit, don't miss a trip to Baikonur. Sputnik, Yuri Gagarin and Dennis Tito, the world's first space tourist, all blasted into space from this empty stretch of Kazakh steppe. Modern rocket launches can still be seen from up to 1,000km away. Make your last major stop the remains of the Aral Sea. Aralsk (Aral town) is understandably bleak, but the ships in the desert make a poignant sight, as does the railway station mosaic commemorating local fishermen's efforts to fight famine in 1920s Russia. Return to Almaty from Kyzylorda, the former Kazakh capital with its attractive Russian Orthodox church, making sure you see the 9th-century caravanserai at Sauran before departing.
If you are lucky enough to have three to four weeks in Kazakhstan, you will have ample time to explore the country and may even consider trekking over the border to Kyrgyzstan to see the best of the Tian Shan Mountains. Consider hiring a car and, having done a trek in the breathtaking Charyn Canyon east of the city, drive north from Almaty to the 614km-long Lake Balkhash. Wild boar, wolves, pelicans and reed cats (Felis chaus) are all present in significant numbers, and the lake's shallow waters are a fisherman's dream. Continuing north, Karaganda provides an insight into more harrowing aspects of Kazakhstan's past: migrants and prisoners slaved here well into the 1950s, forced to exploit the region's mineral wealth. Their stories .lie lold al Ihe Karaganda Regional Historical Museum, and also by the industrial decay that litters the landscape. Break your journey with a few days of indulgence in Astana and marvel at the eccentric architecture of landmarks such as the Palace of Peace and Harmony, the Baiterek observation tower and, of course, Lord Foster's newly completed giant tent (the Khan Shatyr). Providing you are not agoraphobic, you should then work your way west through the central steppe, camping when weather permits to take in some serious stargazing. Keep your eyes peeled for the steppe eagles, marmots and Bactrian camels and head towards Aral, finishing your trip by completing the two-week itinerary in reverse.