1. Hooker, J. T. (2003). Linear B: An introduction. Bristol: Bristol Classical Press.
A very technical book that is meant for those who want to learn Linear B. The introduction and the first section are more accessible to the general reader; however, beyond those sections it gets extremely technical.
2. Robinson, A. (2012). The man who deciphered Linear B: The story of Michael Ventris. London: Thames & Hudson.
This book is meant as a general reading book, examining the life of Michael Ventris the man who deciphered Linear B, his process, and the international attempts of decipherment. It is informative and fun to read.
3. Chadwick, J. (2014). The decipherment of linear B. Cambridge: Canto.
Chadwick corresponded with Michael Ventris during his decipherment of Linear B and himself contributed to the process. This is also a more technical read; however, there are many easy to understand sections sprinkled throughout the technical ones.
Roughly around 1600 BC a unique form of written language develops on mainland Greece, one that is roughly based on the earlier syllabic Minoan Linear A found on Crete. This new language is called Linear B, and was first discovered by Sir Arthur Evans on Crete in 1900 AD. For several decades this language, like Linear A, was undecipherable until 1952 when Michael Ventris cracked it in 1952 AD. While most, including Ventris, sought the source of Linear B outside of Greece it was found by Ventris to be an archaic ancient Greek dialect and the oldest known. The main use of Linear B was for economic and palatial records, recording the input and output of goods and tribute. While most tablets were made to be reusable, many survive due to the destruction at the palaces and their hardening in the fires. Elements of Linear B went on to survive in Homer's poetry and is the base of later Greek language.