Gamboa Mutuberria, José ManuelBujalance, E.Etayo Gordejuela, J. Javier2023-06-212023-06-211986Alling, N. L. and Greenleaf, N.: Foundations of the theory of Klein surfaces. Lect. Notes in Math., vol. 219, Springer (1971). Bujalance, E., Etayo, J. J., and Gamboa, J.M.: Superficies de Klein elipticashiperelipticas. Mem. R. Acad. Ci. (to appear). Groups of automorphism of hyperelliptic Klein surfaces of genus three. Michigan Math. J., vol. 33 (1986). Bujalance, E. Gamboa, J. M.: Automorphism groups of algebraic curves of R of genus two. Arch. Math., 42, 229-237 (1984). Coxeter, H. S. M. and Moser, W. O.J.: Generators and relations for discrete groups. Ergeb. der Math., vol. 14, Springer (4tl ed., 1980). Macbeath, A. M.: The classification of non-Euclidean plane crystallographic groups. Canad. J. Math., 19, 1192-1205 (1967). May, C. L.: Automorphisms of compact Klein surfaces with boundary. Pacific J. Math., $9, 199-210 (1975). Preston, R." Projective structures and fundamental domains on compact Klein surfaces. Ph. D. thesis, Univ. of Texas (1975).0386-219410.3792/pjaa.62.40https://hdl.handle.net/20.500.14352/64623Let C be an algebraic curve of genus 3, defined over the real field R. The automorphism group of C is studied in this paper. In a paper by the same authors [Mich. Math. J. 33, 55-74 (1986; see 20043 below)], the hyperelliptic case was solved, the authors found 5 abstract groups in that case. In the paper under review, a full classification is announced, in which 8 abstract groups appear. A sketch of one of the new cases is given, full proofs appeared in Mem. R. Acad. Cienc. Exactas Fis. Nat. Madrid, Ser. Cienc. Exactas 19 (1985; see the following review)].engjournal articlehttp://projecteuclid.org/euclid.pja/1195514498http://projecteuclid.orgopen access512.7automorphism groups of real algebraic curvesKlein surfacesGeometria algebraica1201.01 Geometría Algebraica