Out of copyright mathematics books

Baker, Arthur Latham - Elliptic Functions: An Elementary Text-Book for Students of Mathematics (1890)

Level: undergraduate

Topics: Elliptic functions

19th century tract on elliptic functions, converted to Latex.

Barnard, Samuel; Child, James Mark - Higher Algebra (1936)

Level: undergraduate

Topics: Number theory, Analysis, Theory of equations

Barnard, Samuel; Child, James Mark - Advanced Algebra (1939)

Level: undergraduate

Boole, George - The mathematical analysis of logic : being an essay towards a calculus of deductive reasoning [1] (1847)

Topics: Logic

Burnside, William - Theory of groups of finite order [1] (1897)

Topics: Group theory

Cajori, Florian - A History of Mathematics [1] (1893)

Topics: History

Cajori, Florian - An Introduction To The Modern Theory Of Equations

Topics: Theory of equations, Galois theory

Carmichael, Robert Daniel - The Theory of Numbers (1914)

Topics: Number theory

Carmichael, Robert Daniel - Diophantine Analysis (1915)

Level: graduate

Topics: Number theory

Monograph on number theory.

Coolidge, Julian Lowell - A treatise on the circle and the sphere (1916)

Topics: Geometry, Differential geometry

Coolidge, Julian Lowell - The Elements Of Non Euclidean Geometry (1909)

Topics: Geometry, Differential geometry

De Morgan, Augustus - Elementary Illustrations of the Differential and Integral Calculus (1899)

Topics: Calculus, Differentiation, Integration

De Morgan, Augustus - On the study and difficulties of mathematics

Level: introductory

Topics: Algebra

Dedekind, Richard - Essays on the Theory of Numbers by Richard Dedekind

Level: monograph

Topics: Number theory

Dickson, Leonard Eugene - History of the theory of numbers

Topics: History, Number theory

Dickson, Leonard Eugene - First Course in the Theory of Equations (1922)

Topics: Theory of equations

Solutions of cubic, quartic polynomials, etc.

Edwards, Joseph - An elementary treatise on the differential calculus, with applications and numerous examples (1896)

Level: university

Topics: Calculus, Differentiation

Differentiation with emphasis on Cambridge Tripos problems

Edwards, Joseph - A treatise on the integral calculus : with applications, examples and problems - volume II (1922)

Topics: Calculus, Integration

Edwards, Joseph - A treatise on the integral calculus : with applications, examples and problems - volume I (1922)

Topics: Calculus, Integration

A thousand pages of integration.

Elliott, Edwin Bailey - An introduction to the algebra of quantics (1913)

"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.

Goursat, Edouard - Derivatives and Differentials (1904)

Topics: Calculus, Differentiation, Differential geometry

Hall, Henry Sinclair; Knight, Samuel Ratcliffe - Higher algebra [1] (1889)

Topics: Algebra

Various topics in algebra which are possibly no longer mainstream parts of the university curriculum. A solutions manual is available by the same authors.

Hall, Henry Sinclair; Knight, Samuel Ratcliffe - Solutions of the examples in Higher algebra [1]

Solutions to Higher Algebra by the same authors.

Hardy, Godfrey Harold - The Integration of Functions of a Single Variable

Level: monograph

Topics: Integration

Tract on integration, including theorems of integrability in terms of elementary functions, elliptic integrals, etc.

Hardy, Godfrey Harold - A course of pure mathematics (1921)

Topics: Analysis

Hart, William - Intermediate algebra for colleges (1948)

Level: secondary

Hathaway, Arthur S. - A Primer of Quaternions (1896)

Topics: Quaternions

Jones, Samuel Isaac - Mathematical Wrinkles (1913)

Topics: Recreational mathematics

Jordan, Camille - Cours d'analyse de l'école polytechnique (1882)

Topics: Analysis

Kaye, George Rusby - Indian mathematics (1915)

Topics: History

Historical treatise on ancient Indian mathematical knowledge.

Keynes, John Maynard - A Treatise on Probability (1921)

Topics: Probability

Klein, Felix - Lectures on Mathematics (1894)

Lagrange, Joseph Louis - Lectures on Elementary Mathematics (1901)

Topics: Number theory, Algebra

MacMahon, Percy Alexander - Combinatory analysis

Topics: Combinatorics

Does not contain "analysis" in the modern sense.

Marks, Constance - Mathematical questions and solutions (1901)

Topics: Recreational mathematics

Recreational mathematics from a 19th century magazine. Includes entries by G. H. Hardy.

McDougall, Alexander Hiram - High school geometry (1920)

Level: secondary

Topics: Geometry

Moritz, Robert E. - A Text Book On Spherical Trigonometry (1913)

Topics: Spherical trigonometry

Nunn, T. Percy - Exercises in algebra (1924)

Level: secondary

Practice for university entrance exams.

Page, James Morris - Ordinary differential equations, with an introduction to Lie's theory of the group of one parameter [1] (1897)

Topics: Ordinary differential equations, Differential equations

Russell, Bertrand; Whitehead, Alfred North - Principia Mathematica Volume III (1913)

Saks - Theory of the integral (1937)

Topics: Lebesgue integration, Measure theory

Smith, J. Hamblin - Riders in Euclid (1910)

Topics: Geometry, Synthetic geometry

Supplementary exercises for Euclid's geometry books.

Todhunter, Isaac - A treatise on the differential calculus, with numerous examples

Topics: Calculus, Differentiation

Todhunter, Isaac - An Elementary Treatise On Laplace's Functions, Lame's Functions, And Bessel's Functions (1875)

The scan at archive.org is extremely poor quality.

Todhunter, Isaac - Spherical Trigonometry (1886)

Topics: Spherical trigonometry

Townsend, Edgar Jerome - Functions Of A Complex Variable (1915)

Topics: Complex analysis

University of Cambridge - Papers set in the mathematical tripos : in the University of Cambridge, 1913-1917 (1919)

Veblen, Oswald; Young, John Wesley - Projective geometry volume 1 (1910)

Topics: Projective geometry, Geometry

Veblen, Oswald; Young, John Wesley - Projective geometry volume II (1918)

Topics: Projective geometry, Geometry

Venn, John - The logic of chance

Topics: Probability

Webster, Arthur Gordon - Dynamics of particles and rigid bodies

Topics: Mechanics

Wentworth, George Albert - Plane Geometry (1899)

Level: secondary

Topics: Geometry, Euclidean geometry

White, William Frank - A Scrap-Book of Elementary Mathematics: Notes, Recreations, Essays

Topics: Recreational mathematics

Whitehead, Alfred North - The axioms of projective geometry (1906)

Topics: Geometry

Whitehead, Alfred North - An Introduction to Mathematics

Level: secondary

Whitworth - Choice and chance

Topics: Probability

Woods, Frederick; Bailey, Frederick - A course in mathematics, for students in engineering and applied science, volume II (1909)