The first name that springs to mind when talking about the decipherment of Linear B script is Michael Ventris. Linear B is the name given to Mycenean Greek script which was found in excavations at Knossos, Mycenae and other sites and is the earliest written form of Greek known. There is also Linear A, which recorded Minoan, and has not yet been deciphered, out of which Linear B developed.
No-one ever mentions Alice Kober, without whose work, Michael Ventris would have had a much more difficult time.
She was an academic, an assistant professor of classics at Brooklyn College and in the 1930s she started studying Linear B inscriptions in her spare time, creating a massive card index system. She even had to make the index cards herself, out of old greetings cards and so on, as paper was scarce in wartime America. What she was doing was cross referencing all the relationships between the characters of the script, and the frequency of their use - all essential work to find out the meaning behind the symbols. At the same time, she was learning a variety of ancient languages, including Hittite, Akkadian, Old Persian, and Chinese. She also studied field archaeology in New Mexico and Greece, and also learned Braille, to transcribe textbooks, library materials and exams for blind students at the college.
In 1946, she won a Guggenheim Fellowship, to study Linear B full time for a year. She spent some time in Oxford, copying inscriptions found by Sir Arthur Evans at Knossos, and she discovered that the language she was transcribing was an inflected one, written in a syllabic script.
She died in 1950, at the age of 43, possibly of cancer, as she was a chain smoker. She had met Michael Ventris once, and reportedly didn't like him, but she did leave him her archive when she died. Michael Ventris took over her work, and discovered that the inscriptions were lists of commodities in Mycenaean Greek two years later. Before he could write a book about how he did it he, too, died - in a car crash at the age of 34.