Virtual Private Network is the logical entity, which is created over a physical infrastructure. It can be setup over another private network such as MPLS or public network such as Internet.
All VPN technologies add extra byte to the packet or frame, which increases the overall MTU so the network links should be accommodated to handle bigger MTU values. VPN technologies work based on encapsulation and decapsulation. For example GRE, mGRE and DMVPN encapsulate IP packets into another IP packet, VPLS and EVPN encapsulates Layer 2 frame into an MPLS packets.
You can run routing protocols over some VPN technologies but not all VPN technologies allow you to run routing protocols. In order to support routing over tunnel, tunnel endpoints should be aware from each other. For example MPLS Traffic Engineer tunnels don’t support routing protocols to run over, since the LSPs are unidirectional which mean Head-end and Tail-end routers are not associated. This will be explained in detail in MPLS chapter.
About VPNs, if you are looking for much more detail knowledge, from design and hands-on perspective, please refer to my VPN Training.