1.0 Network Fundamentals.20%. 1.1 Network Components. 1.1a Router:

I think the best definition of a router is from RFC 1812:

2.2.3 Routers

   In the Internet model, constituent networks are connected together by
   IP datagram forwarders which are called routers or IP routers.  In
   this document, every use of the term router is equivalent to IP
   router.  Many older Internet documents refer to routers as gateways.

   Historically, routers have been realized with packet-switching
   software executing on a general-purpose CPU.  However, as custom
   hardware development becomes cheaper and as higher throughput is
   required, special purpose hardware is becoming increasingly common.
   This specification applies to routers regardless of how they are
   implemented.

   A router connects to two or more logical interfaces, represented by
   IP subnets or unnumbered point to point lines (discussed in section
   [2.2.7]).  Thus, it has at least one physical interface.  Forwarding
   an IP datagram generally requires the router to choose the address
   and relevant interface of the next-hop router or (for the final hop)
   the destination host.  This choice, called relaying or forwarding
   depends upon a route database within the router.  The route database
   is also called a routing table or forwarding table.  The term
   "router" derives from the process of building this route database;
   routing protocols and configuration interact in a process called
   routing.

   The routing database should be maintained dynamically to reflect the
   current topology of the Internet system.  A router normally
   accomplishes this by participating in distributed routing and
   reachability algorithms with other routers.

   Routers provide datagram transport only, and they seek to minimize
   the state information necessary to sustain this service in the
   interest of routing flexibility and robustness.

   Packet switching devices may also operate at the Link Layer; such
   devices are usually called bridges.  Network segments that are
   connected by bridges share the same IP network prefix forming a
   single IP subnet.  These other devices are outside the scope of this document.

When I was first starting to study networking, I bought an old Cisco AGS+ router from a friend who had just passed his CCIE Routing and Switching lab. It was loud and I put it out in the garage to work on it. It would only go up to IOS 11.2. But it did routing protocols eigrp, rip, ospf and bgp. I believe it also did igrp, the precursor to eigrp. I got two of them and connected serial interfaces and learned about the “show controller” command to troubleshoot dce and dte. I connected some switches to the fastethernet interfaces on each router and had a little network with a t1 serial wan link in between them.