Why dynamic routing exists
Static routes are fine for a couple of networks, but they don't scale and they don't heal. Dynamic routing protocols let routers advertise the networks they know and learn paths from their neighbours automatically. When a link fails, the protocol re-converges on a new path without anyone editing a config.
IGP vs EGP
Interior Gateway Protocols (OSPF, EIGRP, IS-IS) run inside one organization's network - an 'autonomous system'. The Exterior Gateway Protocol, BGP, runs between autonomous systems and is what stitches the internet (and cloud/hybrid links) together. Different job, different scale.
OSPF in one breath
OSPF routers form neighbours, flood link-state information into an area, build an identical map (the LSDB), and run Dijkstra's SPF to pick lowest-cost paths (cost is based on bandwidth). To become neighbours, two routers must agree on the area, the subnet, the hello/dead timers, and authentication. A wrong area or mismatched timers is the classic 'adjacency stuck' bug.
Administrative distance: who to believe
If a router learns the same network two ways, it trusts the source with the lower administrative distance: connected 0, static 1, EIGRP 90, OSPF 110, RIP 120. So a static route beats an OSPF route for the same prefix even if OSPF's path looks shorter.
EIGRP and BGP concepts
EIGRP (Cisco) picks a 'successor' (best path) and keeps a 'feasible successor' as a loop-free backup for instant failover. BGP doesn't use bandwidth cost at all - it chooses paths by policy attributes (local preference, AS-path length, MED, and more), which is why cloud and multi-ISP routing is about policy, not speed.