Textile factories significantly grew during the First Industrial Revolution, especially british ones.
The growing demand for clothing and cloth was satisfied by the integration of machinery in the factory system. In fact, several inventions in textile machinery occurred in a relatively short time period during the Industrial Revolution. Since they made weaving cloth and spinning yarn and thread much easier, producing cloth became faster and required less time and far less human labor.
Here is a timeline highlighting the most interesting innovations:
Flying shuttle: invented by John Kay: an improvement to looms that enabled weavers to weave faster.
Cotton mills were first opened in England.
Spinning jenny invented by James Hargreaves: the first machine to improve upon the spinning wheel, patented in 1770.
Richard Arkwright patented the water frame: the first powered textile machine.
The first all-cotton textiles were produced in factories.
Crompton invented the spinning mule that allowed for greater control over the weaving process.
Cartwright patented the power loom. It was improved upon by William Horrocks, known for his invention of the variable speed batton in 1813.
Samuel Slater brought textile machinery design to the United States, spreading for the first time the effects of the british industrial revolution.
Arkwright built the first steam-powered textile factory in Nottingham, England.
Eli Whitney invented the cotton gin: the machine that automated the separation of cottonseed from the short-staple cotton fiber.
Joseph Marie Jacquar invented the Jacquard Loom that weaved complex designs. Jacquard invented a way of automatically controlling the warp and weft threads on a silk loom by recording patterns of holes in a string of cards.
image source: http://historicdress.org/omeka/items/show/331
William Horrocks invented the variable speed batton for an improved power loom.
William Perkin invented the first synthetic dye.