The article deals with the early stages of research by Józef Tomasz Rostafinski (1850-1928), one of the greatest Polish biologists, a well-known botanist and humanist. Presented in the article is the correspondence between Rostafinski, and his friend and teacher, the French scientist Jean Baptiste Edouard Bornet (1828-1911). This correspondence is of great value for the assessment of Rostafinski's early research on algae. The correspondence is stored at a library at the Laboratory of Cryptogamy of the National Museum of Natural History in Paris, consituting a small but homogenous and very interesting collection. It consists of eleven well-preserved manuscripts in the French language, which are kept among the materials connected with Edouard Bornet. The letters in the correspondence concern a number of topics, including scientific analysis, descriptions of J. Rostafinski research on algae, numerous questions connected with Laminariaceae, as well as other issues, relating to Rostafinski's friend, E. Janczewski, to the Villa Thuret in France, and to the problems with his mail that Rostafinski experienced in March 1876. It is well known that a major study by Rostafinski was lost and disappeared before its publication - the study in question was a large monograph of the Laminariaceae family of algae, which earned Rostafinski a gold medal in a competition organized by the Royal Academy of Sciences in Brussels in 1877. A new trace of the monograph can be found in his letters to Bornet, in which there is reflected a fragment of an authentic report on the algae research. The letters also contain references ot the work of other scientists, e.g., G. Thuret (1817-1875), E. Janczewski (1846-1918), A. de Bary (1831-1888), A. de Jolis (1823-1904) and M. Woronin (1838-1903).