Mash Tun

The mash tun is the vessel in which the mash is conducted.  It can be a kettle, a converted keg, a cooler, a bucket or other forms.  The grains and hot water (liquor) is added to the mash tun and allowed to rest until the enzymes in the malt have converted the starches in the mat to fermentable sugars.  Most of the time in homebrewing, the mash tun is fitted with a filtering system to separate the sweet wort from the grain.  This is known as a mash/lauter tun (MLT), since it allows you to both mash and lauter in the same container.  A cooler is popular for a MLT, as can be seen here.