Whilst for extract brewing a 2 or 3 gallon boiler or large pan is sufficient, for all grain brewing a boiler of at least 5 1/2 gallons is needed to make 5 gallons of beer, and 6 or 7 gallons is better, to avoid having to keep topping up the boil to replace liquid lost in evaporation.
Plastic Bucket Boiler
The simplest and cheapest method is to use a suitable plastic bucket fitted with a kettle element, and a tap with some sort of hop strainer fitted to it. These can be bought ready made from homebrew shops or you can make one yourself if you are handy.
Stainless Steel Boilers
Whilst these can also be bought ready-made, it's more fun to shop around on ebay for one of the many different stainless steel stockpots that are available. Simply (!) drill holes for your element and tap and you're away. They are also much more shiny than plastic boilers!
You can find details and pictures of how various brewers have made both plastic and stainless boilers on the forum (see link below).
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