Nowadays when we think of a steam engine we have in mind an engine that releases steam under pressure into a cylinder, pushing a piston. Hardly anyone remembers that the basics for the modern steam engine were laid by releasing steam at relatively low pressure into a vessel and condensing the steam in the vessel by rinsing the outside of the vessel with cold water. This caused the steam inside the vessel to condense, which created a vacuum inside the vessel. The vacuum  then was used to suck water upwards. This last principle was used by Thomas Savery in several installations and thus was the first commercially applied use of a steam powered engine. 

The Steam Engine

As soon as miners had to dig deeper to excavate coal, or any other mineral, they were faced with groundwater. They had to use pumps, operated by workers or operated by horses. The proprietor of a colliery at Griff, in Warwickshire, for example employed 500 horses, at an expense of 900£ a year [1]. Apart from the costs the stables for 500 horses must have taken quite a space. Steam operated devices were the answer to this problem.

: condenser
year
1698Thomas Savery: atmospheric water pump
1712Newcomen: piston and balancier
1765Smeaton's optimization of the Newcomen steam engine
1765James Watt
1781Jonathan Hornblower: compound steam engine
1799Richard Trevithick: high pressure steam engine
1800James Watt's condenser patents expires
1849George Henry Corliss: Corliss-type steam engine
1862The Allen steam engine (later called Porter-Allen)
1884Charles Algernon Parsons: steam turbine

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[1] John, Farey, A treatise on the steam engine : historical, practical, and descriptive, London 1827, page 128; available INTERNET ARCHIVE