There are three principal thickening agents used in the production of sauces and a few others which are far less commonly used.
A roux uses the starch in flour to to thicken the sauce. This starch cannot easily be accessed as the starch grains have thick walls which must be broken down to access the starch.
In order to access the starch, the flour is heated in fat. The boiling stock is not hot enough to do this.
The fat is melted (butter or margarine is most common) and gently heated. Plain flour is then added and cooked gently in the fat until the texture changes to look like wet sand. At this point the grains of starch have been broken down and the starch can now be accessed to thicken the sauce.
Depending on the sauce to be produced the Roux may be cooked for a longer time. There are three grades of roux depending on use.
Cooked for 2-3 minutes until the flour is "cooked out". This means that the starch grains have been broken down (the sandy texture) but the flour has not been coloured and will not affect the colour of the finished sauce.
A blonde roux is cooked for between 3-5 minutes. The flour will be cooked out and the colour will change to a pale brown colour - the roux will be sandy in colour and texture. This will give a darker colour to the finished sauce.
The roux is cooked for up to 10 - 15 minutes until it is nut brown in colour. Care should be taken to avoid actually burning the roux in this case.
This is an equal mix of flour and fat (butter or margarine) which is mixed together to form a paste. Small pieces are then added to the sauce as it cooks out.
This is also known as a cold roux or pounded butter.
Other thickening agents include arrowroot, corn flour, potato flour, rice flour and barley flour.
Arrowroot and corn flour are the most common.
The starch is mix with cold water first and it is then added slowly into the stock thickening as the temperature increases.
If the starch is added without first being mixed with cold water, it will form lumps in the sauce which will not dissolve.
Other agents include:
Vegetables and fruit
Blood (as in jugged hare)