These links will take you to pages at The MacTutor History of Mathematics. The list includes names mentioned in our textbook
Abstract Algebra.

Abel, N. (1802-1829)
Archimedes, (BC 287-212)
Artin, E. (1898-1962)

Boole, G. (1815-1864)
Burnside, W. (1852-1927)

Cardano, G. (1501-1576)
Cauchy, A. (1789-1857)
Cayley, A. (1821-1895)

d'Alembert, J. (1717-1783)
Dedekind, R. (1831-1916)
del Ferro, S. (1465-1526)
de Moivre, A. (1667-1754)
DeMorgan, A. (1806-1871)
Descartes, R. (1596-1650)
Diophantus (~200-284)

Eisenstein, G. (1823-1852)
Eratosthenes (BC 276-194)
Euclid (BC ~325-265)
Euler, L. (1707-1783)

Fermat, P. (1601-1665)
Ferrari, L. (1522-1565)
Fibonacci, L. (1170-1250)
Fourier, J. (1768-1830)
Frobenius, G. (1849-1917)

Galois, E. (1811-1832)
Gauss, C. (1777-1855)
Goldbach, C. (1690-1764)

Hermite, C. (1822-1901)
Herstein, Y. (1923-1988)
Hilbert, D. (1862-1943)
Hölder, O. (1859-1937)

Jordan, C. (1838-1922)

Khwarizmi, A. (~780-~850)
Khayyam, O. (1048-1131)
Klein, F. (1849-1925)
Kronecker, L. (1823-1891)
Kummer, E. (1810-1893)

Lagrange, J. (1736-1813)
Lamé, G. (1795-1870)
Legendre, A. (1752-1833)
Lindemann, C. (1852-1939)
Liouville, J. (1809-1882)
Lorentz, H. (1853-1928)

Mersenne, M. (1588-1648)
Möbius, A. (1790-1868)

Noether, E. (1882-1935)

Pascal, B. (1623-1662)
Peano, G. (1858-1932)
Pythagorus, (BC 569-475)

Ruffini, P. (1765-1822)

Sylow, L. (1832-1918)

Tartaglia, N. (1499-1557)

Thompson, J. (1932- )

Vandermonde, (1735-1796)
Viète, F. (1540-1603)

Weber, H. (1842-1913)
Wedderburn, (1882-1948)
Wiles, A. (1953- )
Wilson, J. (1741-1793)

Important note: the above links lead to pages at The MacTutor History of Mathematics archives.