Available on the internet are scans of tatting books written as far back as the 1850s. We owe a debt of gratitude to the volunteers who do the work of scanning these treasures:
A few examples from these archives are:
“Tatting or Frivolité” by Mrs Mee and Miss Austin, published in 1850
“Tatting” by Mlle Riego, 1850, followed by 9 more of the little books she published from 1861-8, and a final one in 1886.
“The Lady's Manual of Fancy Work”, by Mrs Pullan, 1859. Has small but historically interesting section on tatting.
“The Bath Tatting Book” by P. P., 1865
“Book of Needlework” by Mrs Beeton, published in 1870. It has 80 pages of tatting patterns. Issued as a reprint in the 1980s, also available from The Gutenberg Project (see above).
“Encyclopedia of Needlework” by Thérèse de Dillmont, published in 1886. Has 24 pages of tatting patterns.
We can also buy reprints of actual books filled with patterns from the early 20th century, thanks to Dover Publications, for example:
They are paperback and only cost a few pounds or dollars. Even if you don't want to tat traditional doilies, these patterns can provide inspiration for a more modern take on tatting.