Out of copyright mathematics books
See the bottom of the page for explanatory notes and links to other sites with more lists and information.
List of books
Elliptic Functions: An Elementary TextBook for Students of Mathematics (1890)  Baker, Arthur Latham
19th century tract on elliptic functions, converted to Latex.
Higher Algebra (1936)  Barnard, Samuel; Child, James Mark
Number theory etc.
Advanced Algebra (1939)  Barnard, Samuel; Child, James Mark
The mathematical analysis of logic : being an essay towards a calculus of deductive reasoning [1] (1847)  Boole, George
Theory of groups of finite order [1] (1897)  Burnside, William
The Theory of Numbers (1914)  Carmichael, Robert Daniel
Diophantine Analysis (1915)  Carmichael, Robert Daniel
Monograph on number theory.
A treatise on the circle and the sphere (1916)  Coolidge, Julian Lowell
The Elements Of Non Euclidean Geometry (1909)  Coolidge, Julian Lowell
Elementary Illustrations of the Differential and Integral Calculus (1899)  De Morgan, Augustus
The author died in 1871, so this is a reprint. The author is the De Morgan of De Morgan's laws for intersections and unions of sets.
History of the theory of numbers  Dickson, Leonard Eugene
First Course in the Theory of Equations (1922)  Dickson, Leonard Eugene
Solutions of cubic, quartic polynomials, etc.
An elementary treatise on the differential calculus, with applications and numerous examples (1896)  Edwards, Joseph
Differentiation with emphasis on Cambridge Tripos problems
A treatise on the integral calculus : with applications, examples and problems  volume II (1922)  Edwards, Joseph
A treatise on the integral calculus : with applications, examples and problems  volume I (1922)  Edwards, Joseph
A thousand pages of integration.
An introduction to the algebra of quantics (1913)  Elliott, Edwin Bailey
"Quantic" is an older name for "homogeneous polynomial" or "form", as in "quadratic form", a polynomial in more than one variable, such as $x^2+y^2$, where the exponents are all equal.
Derivatives and Differentials (1904)  Goursat, Edouard
Higher algebra [1] (1889)  Hall, Henry Sinclair; Knight, Samuel Ratcliffe
Various topics in algebra which are possibly no longer mainstream parts of the university curriculum. A solutions manual is available by the same authors.
Solutions of the examples in Higher algebra [1]  Hall, Henry Sinclair; Knight, Samuel Ratcliffe
Solutions to Higher Algebra by the same authors.
The Integration of Functions of a Single Variable  Hardy, Godfrey Harold
Tract on integration, including theorems of integrability in terms of elementary functions, elliptic integrals, etc.
A course of pure mathematics  Hardy, Godfrey Harold
Intermediate algebra for colleges (1948)  Hart, William
A Primer of Quaternions (1896)  Hathaway, Arthur S.
Mathematical Wrinkles (1913)  Jones, Samuel Isaac
Recreational mathematics
Cours d'analyse de l'école polytechnique (1882)  Jordan, Camille
Indian mathematics (1915)  Kaye, George Rusby
Historical treatise on ancient Indian mathematical knowledge.
A Treatise on Probability (1921)  Keynes, John Maynard
Combinatory analysis  MacMahon, Percy Alexander
Mathematical questions and solutions (1901)  Marks, Constance
Recreational mathematics from a 19th century magazine. Includes entries by G. H. Hardy.
High school geometry (1920)  McDougall, Alexander Hiram
A Text Book On Spherical Trigonometry (1913)  Moritz, Robert E.
Exercises in algebra (1924)  Nunn, T. Percy
Practice for university entrance exams.
Ordinary differential equations, with an introduction to Lie's theory of the group of one parameter [1] (1897)  Page, James Morris
Principia Mathematica Volume III (1913)  Russell, Bertrand; Whitehead, Alfred North
Theory of the integral (1937)  Saks
Lebesgue integration and measure theory.
Riders in Euclid (1910)  Smith, J. Hamblin
Supplementary exercises for Euclid's geometry books.
A treatise on the differential calculus, with numerous examples  Todhunter, Isaac
An Elementary Treatise On Laplace's Functions, Lame's Functions, And Bessel's Functions (1875)  Todhunter, Isaac
The scan at archive.org is extremely poor quality.
Spherical Trigonometry (1886)  Todhunter, Isaac
Functions Of A Complex Variable (1915)  Townsend, Edgar Jerome
Papers set in the mathematical tripos : in the University of Cambridge, 19131917 (1919)  University of Cambridge
Projective geometry volume 1 (1910)  Veblen, Oswald; Young, John Wesley
Projective geometry volume II (1918)  Veblen, Oswald; Young, John Wesley
Dynamics of particles and rigid bodies  Webster, Arthur Gordon
Plane Geometry (1899)  Wentworth, George Albert
The axioms of projective geometry (1906)  Whitehead, Alfred North
A course of modern analysis (1915)  Whittaker, E. T.
Choice and chance  Whitworth
A course in mathematics, for students in engineering and applied science, volume II (1909)  Woods, Frederick; Bailey, Frederick
List of authors
 Bailey, Frederick 49
 Baker, Arthur Latham 1
 Barnard, Samuel 2 3
 Boole, George 4
 Burnside, William 5
 Carmichael, Robert Daniel 6 7
 Child, James Mark 2 3
 Coolidge, Julian Lowell 8 9
 De Morgan, Augustus 10
 Dickson, Leonard Eugene 11 12
 Edwards, Joseph 13 14 15
 Elliott, Edwin Bailey 16
 Goursat, Edouard 17
 Hall, Henry Sinclair 18 19
 Hardy, Godfrey Harold 20 21
 Hart, William 22
 Hathaway, Arthur S. 23
 Jones, Samuel Isaac 24
 Jordan, Camille 25
 Kaye, George Rusby 26
 Keynes, John Maynard 27
 Knight, Samuel Ratcliffe 18 19
 MacMahon, Percy Alexander 28
 Marks, Constance 29
 McDougall, Alexander Hiram 30
 Moritz, Robert E. 31
 Nunn, T. Percy 32
 Page, James Morris 33
 Russell, Bertrand 34
 Saks 35
 Smith, J. Hamblin 36
 Todhunter, Isaac 37 38 39
 Townsend, Edgar Jerome 40
 University of Cambridge 41
 Veblen, Oswald 42 43
 Webster, Arthur Gordon 44
 Wentworth, George Albert 45
 Whitehead, Alfred North 34 46
 Whittaker, E. T. 47
 Whitworth 48
 Woods, Frederick 49
 Young, John Wesley 42 43
Notes
This is a list of outofcopyright mathematics books which can be found on sites like the Internet Archive (archive.org) or Project Gutenberg (gutenberg.org). The year of each publication is the year of the edition rather than the printing. The books are ordered by the author's surname. Where more than one different copy of the book could be located, the multiple links are numbered [1], [2], etc.
I have mostly omitted the following types of resources:
 Business mathematics, "Practical man" mathematics
 Texts on pedagogy ("Teaching of mathematics" etc.)
 Journals
 Theses
 Tables, such as trigonometric or logarithm tables
 Very introductory books
 Collections of papers
I've also skipped over some old mathematical physics and engineering books.
The books are not yet categorised. You may download the original file which contains some more information here. This is formatted in my Table::Readable format.
Some of the books have been inputted by various different institutions, so there may be other copies, scanned in a different manner, at the sites.
Web links

Free Public Domain Ebooks
A list of books like this one, made by one of the members of Project Gutenberg (Thank you for your hard work!)

Project Gutenberg Books in Mathematics
There are various other books here not mentioned above.

Cornell University Library Digital Math Monographs
A digital collection of historical math monographs. This was the source used by at least some of the Project Gutenberg maths books and also archive.org. However, it restricts access to some of the material which is visible on archive.org.

Hathi Trust Digital Library
Contains digitized books from multiple academic libraries.

The University of Michigan Historical Mathematics Collection
Various outofcopyright monographs. It's not very easy to navigate.