Running bitcoin core in a low storage system I have a machine with ~40GB in storage. The Bitcoin block chain is ~75GB in size, is there any chance to run bitcoind in my system? I mean, can I somehow skip downloading some part of the block chain?

Thanks in advance for any answers.
You cannot skip downloading the blockchain, but you can skip storing it.

If you run Bitcoin Core with the -prune=N or put prune=N in the bitcoin.conf file, only at most N megabytes worth of blocks will be stored on disk. N has to be at least 550 currently.

Pruning does not reduce the validation or security at all, but does prevent your node from serving historical blocks to other peers.