Sometimes trees have to be removed (e.g. due to structural damage or disease). After a tree has been cut down, a 'stump' is usually left. This consists of the roots the very bottom of the trunk (typically less than a foot of the trunk).
Stumps and their related root systems take up space, and it is usually desirable to remove them.
Stumps are typically dug out, shredded insitu using a stump grinder, burnt, or treated chemically. Chemical products are typically based on potassium nitrate (salt petre) and work by rapidly increasing the rate of decay. A stump so treated has typically rotted into manageable pieces in about 4-6 weeks. Potassium Nitrate followed a few weeks later with fire is also effective as the potassium nitrate acts as an oxidiser (some jurisdictions may control the distribution of larger quantities potassium nitrate).
Use this tag for all questions about removing the tree stumps. The tag can also be used for all woody stump removal even if they are not technically trees (eg. shrub stumps).