Moscow (Russian: Москва, Moskva) is Russia's capital.
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East towards Vladimir, Nizhny Novgorod, the Far East
Take the metro to the station Shosse Entuziastov (Шоссе Энтузиастов). From there, walk up to the main street and you'll directly be at the bus stop. Here, take bus #702 or #214 to Southern Izmaylovo (южное Измайлово). Get out at the last stop. Here you can already hear the highway, though it's a bit difficult to find it in first place. Walk back in south-eastern direction until you'll find a McDonalds restaurant. This is directy located at the highway junction of the ring. Walk for around 150m east down under the bridge until you find a good spot to start hitchhiking. Additionally, you can also walk 300m further until the petrol station and start hitchhiking on the hard shoulder just behind it. Traffic here is huge.
Take the metro to the station Yugo-Zapadnaya and then take bus #707 or #611 to the stop Dudkino. You can hitchhike directly from the bus stop. This is the highway Kievskoe shosse that goes all the way to Kyiv. Soon the highway becomes a simple two-lane road, so that even if your driver must drop you off only after a few dozen kilometres, you can simply remain beside the road and soon get another lift onward.
Other possibility is to take a train (elektrichka) to a small town Aprelevka (look at the map) - it is directly situated on the M3 highway Moscow/Kiev. Just walk 1 km to the highway (ask people about the direction). However, cars here move fast.