There are five different Networking Topologies :

A) Bus

B) Star

C) Ring

D) Mesh

E) Tree.
When networks are design using multiple topologies it is called Hybrid Networks, this concept is usually utilized in complex networks were larger number of computer clients are required.
Bus Topology:
Bus topology is one the easiest topologies to install, it does not require lots of cabling. There are two most popular Ethernet cable types which are used in this topology they are 10Base-2 and 10BaseT. Bus topology based networks works with very limited devices. It performs fine as long as computer count remain with in 12 – 15, problems occurs when number of computer increases.Bus topology uses one common cable (backbone) to connect all devices in the network in linear shape. Network interface cards of all network devices are attached to single communication medium backbone cable. When any computer sends out message in the network it is broadcasted in the entire network but only intended computer accepts the message and process it. Bus topology provide simplicity to the network, however there is big disadvantage of this topology, if main single network cable some how gets damaged, it will shut down the entire network no computer will run on network and no communication can be made among computers until backbone cable is replaced.

Ring Topology:

Ring topology is one of the old ways of building computer network design and it is pretty much obsolete. FDDI, SONET or Token Ring technologies are used to build ring technology. It is not widely popular in terms of usability but incase if you find it any where it will mostly be in schools or office buildings. In ring network topology computers and other networking devices are attached to each other in such a way that they have devices adjacent to each other (Left and right side). All messages are travelled in the same directory either clockwise or anticlockwise. In case of failure of any device or cable the whole network will be down and communication will not be possible.

Star Topology:

This is the most commonly used network topology design you will come across in LAN computer networks. In Star, all computers are connected to central device called hub, router or switches using Unshielded Twisted Pair (UTP) or Shielded Twisted Pair cables.In star topology, we require more connecting devices like routers, cables unlike in bus topology where entire network is supported by single backbone. The most practical point of Star topology success is that the entire network does not go down incase of failure of a computer or cable or device, it will only affect the computer whose wire failed rest of the network will be working fine. However, incase of failure of central communication device such as Hub, Router or Switch the entire network will collapse. Star topology is widely used in homes, offices and in buildings because of its commercial success.
Tree Topology:

Just as name suggest, the network design is little confusing and complex to understand at first but if we have better understanding of Star and Bus topologies then Tree is very simple. Tree topology is basically the mixture of many Star topology designs connected together using bus topology. Devices like Hub can be directly connected to Tree bus and each hub performs as root of a tree of the network devices. Tree topology is very dynamic in nature and it holds potential of expandability of networks far better than other topologies like Bus and Star.

Mesh Topology:

Mesh topology is designed over the concept of routing. Basically it uses router to choose the shortest distance for the destination. In topologies like star, bus etc, message is broadcasted to entire network and only intended computer accepts the message, but in mesh the message is only sent to the destination computer which finds its route it self with the help of router. Internet is based on mesh topology. Routers plays important role in mesh topology, routers are responsible to route the message to its destination address or computer. When every device is connected to every other device it is known as full mesh topology and if every device is connected indirectly to each other then it is called partial mesh topology.

Conclusion:

Topologies are essence of computer networks design. Efficent networks can only be built based on the complete knowledge and understanding of above mentioned topologies. Knowledge of every communication device is of equal importance to help you find the best option for your network requirements. Optimum networks can be built with complete knowledge and understanding of computer network devices and how they are designed, any mistake in choosing inappropriate techniques, device etc can only be the waste of time, resources and efforts.