Air
Kursk located only a few hundreds km from Moscow is so well connected by bus and rail to the capital of Russia, that you will not perhaps want to fly. Nevertheless, there are regular flights to/from Moscow and St. Petersburg.
Train
Kursk is on the Moscow -Kharkiv railway with trains to Moscow every half-hour (8 hours) and Kharkiv (3 hours). There are also daily trains to/from the Caucasus and Crimea.
Bus
Kursk is also accessible by bus from Belgorod, Oryol, Moscow and Kharkiv.