There are many different ways of describing a change ringing method. The simplest one is to write out all the changes in order. This allows someone to look for certain changes that they consider musical and allows inspection for falseness, but it is more information than most people can easily remember.
In a normal ringing method, all the working bells do the same work (follow the same pattern), so describing the path of a single bell through the method is enough to describe what all the bells do (the non-working bells follow a different path, which is often much simpler). The path of a bell can be described in words, with descriptions of where it hunts, dodges, reverse hunts, and does other various maneuvers, but these get lengthy and can be very confusing until the ringer has learned all the terms. An easier way to describe the path of a bell is to write out all the changes of the method and then draw a line through the path of a bell. For historical reasons this path is called a blue line and is often drawn to follow the path of the largest bell (the tenor). Ringers learn the blue line when learning a method, and follow the line (mentally) when they are ringing.
Another way to describe a ringing method is to describe how each row is permuted to get the next row. The rules of change ringing methods make it very easy to describe these permutations. Each bell can only move one place per change, and every bell has to sound in every row. This means that there are only three things a bell can do when going from one row to the next: stay in the same place, move up one place, or move down one place. Additionally, if one bell is moving up, then the next bell must move down, and conversely, if one bell is moving down, then the previous bell must be moving up. In other words, bells swap in pairs between the bells that are not moving. Listing either the bells that move or the bells that don't move is enough to describe how to change one row to the next one. Since ringers want to move as many of the bells as possible each change, there are more bells being swapped than staying still, so listing the bells that stay still is easier. This notation for describing a method is called place notation because it describes which bells are making a place (staying in that place for two consecutive changes).
If all the bells are swapping, the place notation is written as an x. Otherwise the bells that are not moving are listed. Dots are used to seperate the lists of numbers. For example, 5.1.5.1.5.1.5.1.5.1 is the place notation for plain hunt on 5, and x16x16x16x16x16x16 is the place notation for plain hunt on 6.
Change Ringing Methods are classified based on how many bells are in the method and what the hunt bells (if any) do. Methods with no hunt bells are called principals if all the bells do the same work, otherwise they are differential. If there is only one hunt bell, then the method is a plain method if the hunt bell plain hunts, a treble bob, surprise, or delight method if the hunt bell bob hunts, a treble place method if the hunt bell makes places, an alliance if the hunt bell does not have the same number of blows in each position, and a hybrid if the hunt bell is not symmetrical about the half lead. Double methods have symmetrical work back to front. There are more rules for naming methods on the Central Council of Church Bell Ringers rules web page. The number of bells determines the stage of the method. The stages have the following names