Bitcoin core stopped sync'ing (without downloading all the data). How can I make it resume the synchronization? I am extremely new to this concept but just decided to try. Unfortunately I did not do my homework before playing with my money.
I bought some coins and I sent them to my Bitcoin core wallet (that I had just installed, knowing nothing about the fact that it needed to sync first). I realized that since it wasn't synchronized I would need to wait until it finished downloading all of the data for me to have access to that money. 

the problem is that my bitcoin core just stopped downloading data with the loading bar still in the middle and it is no longer synchronizing.

How can I make my bitcoin core complete to download all the data?
There are pretty much two stages. The first stage is to download (catch up) the whole blockchain that has 64.4 GB.

Once you have that the verification stage checks all payments ever made.

Both these things are pretty painful but once both are done you can backup your blockchain for example to external disk and you won't ever have to do it again.

Don't delete your wallet file.  Backup your wallet.dat file.  

So delete everything, restart bitcoin, let it run for a few days and hope it doesn't get stuck.

Good luck.

Edit: do you have enough free disk space?

Edit2: don't delete the wallet