We can have two types: Physical and logical topologies.
When talking about physical topologies, this refers to the way the "physical" devices are arranged; e.g. Routers, Switches and Hubs.
Logical topology refers to the way data flows across a network.
We have 4 "main" network topologies:
1. BUS TOPOLOGY: In bus topology, all computers share a common "bus". Think of this like a single wire, where various users "tap" at various points in order to gain connectivity. This is really a very old kind of set up.
Bus Topology, Source: www.tutorialspoint.com
2. RING TOPOLOGY: A ring topology setup will see computers connected in a loop. One computer is connected to the next, and so on; in a ring layout.
Ring topology, Source: Google
Using this kind of layout on a network has disadvantages too. Once there a failure in any of the links, it could fully cut of full network connectivity.
3. STAR TOPOLOGY: This topology is the most popular example of network topologies. In this kind of topology, there is usually a central device, such as a switch or hub, where all computers on the network connect to.
Star Topology, Source: Google
This kind of network layout usually permits more than one device to transmit at a time.
4. MESH TOPOLOGY: This is a network topology in which computers are connected to one another so that all computers can access each other and share information.
Mesh Topology: Source: www.technologyuk.net
A mesh topology layout is expensive, considering the cost of cabling, and considering the fact that computer systems usually come with only one Network Interface Card (where you plug in your network cable); hence, you would have to purchase additional units of those.
Mesh topology can be either partial mesh or full mesh.
Partial mesh allows some computer systems to be connected to all others, while full mesh ensures that every computer on the network is connected to every other computer (such as in the diagram above)
There are other network topologies that exist, such as the extended star (which consists of multiple star topologies connected together); but all are based on the four mentioned above.