Hello!
Shogun 2 is set in the Sengoku Period in Japan. As the game suggests, a lot of fighting took place during that time and it was the golden age of the Samurai. We are offered a short introductary cutscene at the beginning of the game and a text about each playable clan, but more detailed information about the society and politics of the time, as well as how history unfolded in reality, has to be searched for outside of the game. If you are searching for such information, I hope to be able to help you with this list! I have added the few books I have read myself as well as those that seem to be generally respected by historians and the public. Also I included a lot of Osprey Publishing books because they specify in military history and that is what we Shogun 2 players probably care about most.
The list is divided into three parts:
The first part contains books that focus only on warfare and politics in the Sengoku Period in Japan and explain it in general. Those are probably the books most interesting to Shogun 2 players, as that are the topics the game is about. The books are listed with author, publisher and their synopsis text from a website they are available on.
In the second part, there are books on the history of the Samurai in general, not just focusing on the Sengoku Period. They are listed like in the first part.
In the third part, I collected books that are about very specific themes like individual weapons, units or battles and stuff like that. I did not include the synopsis texts for them because most titles are self explanatory.
If you know any books that should be added to this list, please comment. I hope you find something good to read here!

• Samurai Armies 1467–1649. Stephen Turnbull, Osprey Publishing
  The Sengoku The Jidai, 'Age of Warring States', is the age of the samurai the military aristocracy of Japan. This period, which lasted from the outbreak of the Onin War in 1467 to the establishment of the Tokugawa Shogunate in the early 17th century, was a period of endemic warfare, when a lack of central control led to constant struggles between the daimyo, 'great names', who sought to extend the influence of their families through political and military means. This title will examine the complicated nature of family and clan that governed so much of the initial organization of the armies, how this changed over the period and how battlefield tactics developed over a series of major encounters such as Nagashino and Sekigahara.

• Samurai Armies 1550–1615. Stephen Turnbull, Osprey Publishing
  In 1543 three Portuguese merchants entered a turbulent Japan, bringing with them the first firearms the Japanese had ever seen: simple matchlock muskets called arquebuses. They proved a decisive addition to the Japanese armoury, as for centuries the samurai had fought only with bow, sword and spear. In 1575, one of the greatest original thinkers in the history of samurai, Oda Nobunaga, arranged his arquebusiers in ranks three deep behind a palisade and proceeded, quite literally, to blow his opponent's cavalry to pieces, marking the beginning of a new era in Japanese military history.

• Samurai 1550–1600. Anthony J Bryant, Osprey Publishing
  This title details the culture, weapons, armour and training of the elite samurai warrior class in the fascinating Age of Battles period (1550-1600). This was a period of vital importance not only because of the political effects of the chaos but also due to the changes in warfare that occurred. In 1542 the Portuguese introduced the matchlock musket into Japanese warfare, and this book traces the effect that this important innovation had on the samurai. Life outside the field of battle is also examined, making this an unmissable book for those interested in this brave warrior caste.

• Sengoku Jidai. Nobunaga, Hideyoshi, and Ieyasu: Three Unifiers of Japan. Danny Chaplin, CreateSpace Independent Publishing
  Japan's Sengoku jidai ('Warring States Period') was a time of crisis and upheaval, a chaotic epoch when the relatively low-born rural military class of 'bushi' (samurai warriors) succeeded in overthrowing their social superiors in the court throughout much of the country. Into this tumultuous age of constant warfare came three remarkable individuals: Oda Nobunaga (1534-1582), Toyotomi Hideyoshi (1537-1598), and Tokugawa Ieyasu (1543-1616). Each would play a unique role in the reunification of the disparate, fragmented collection of warring provinces which constituted Japan in the sixteenth and early seventeenth centuries.
  
  This new narrative history of the sengoku era draws together the epic strands of their three stories for the first time. It offers a coherent survey of the Azuchi-Momoyama Period (1568-1600) under both Nobunaga and Hideyoshi, followed by the founding years of the Tokugawa shogunate (1600-1616). Every pivotal battle fought by each of these three hegemons is explored in depth from Okehazama (1560) and Nagashino (1575) to Sekigahara (1600) and the Two Sieges of Osaka Castle (1614-15).
  
  In addition, the political and administrative underpinnings of their rule are also examined, as well as the marginal role played by western foreigners ('nanban') and the Christian religion in early modern Japanese society. In its scope, the story of Japan's three unifiers ('the Fool', 'the Monkey', and 'the Old Badger') is a sweeping saga encompassing acts of unimaginable cruelty as well as feats of great samurai heroism which were venerated and written about long into the peaceful Edo/Tokugawa period.

• Sengokujidai: Autonomy, Division and Unity in Later Medievil Japan. Michael Lorimer, Olympia Publishing
  In the mid-15th Century Japan began to face challenges it had never before experienced with such intensity. In the following hundred and fifty years, the so-called 'Age of Warriors' reached its brutal zenith - the imperial court was ignored, the shogun distracted and the population increasingly vociferous. It was the dawning of a nationwide era of families divided and neighbours at war, religious fervour and revolutionary undertones, craftsmen under arms and landlords threatened. In this portrait of a nation divided, Michael Lorimer surveys and explains the multiple trends and events that tore the fabric of state and the lives of people asunder. He then discusses the personalities and factions who brought this world under their sword; the smashing of rival hegemonies and the obliteration of obstructive forces, the destruction of local customs and the flourishing of arts and urban confidence; a time of pleasure, pain and paranoia.

• The Samurai, A Military History. Stephen Turnbull
  First published in 1977, The Samurai has long since become a standard work of reference. It continues to be the most authoritative work on samurai life and warfare published outside Japan. Set against the background of Japan's social and political history, the book records the rise and rise of Japan's extraordinary warrior class from earliest times to the culmination of their culture, prowess and skills as manifested in the last great battle they were ever to fight - that of Osaka Castle in 1615.

• Samurai, The World of the Warrior. Stephen Turnbull, Osprey Publishing
  Stephen Turnbull, the world's leading authority on the samurai, goes beyond the battlefield to paint a picture of the samurai as they really were.
  
  This book explores the samurai within the context of an all-encompassing warrior culture that was expressed through art and poetry as much as through violence.
  
  Using themed chapters, Turnbull illuminates the samurai through their historical development and their relationship to the world around them – relationships that are shown to persist in Japan even today.

• The Samurai. Stephen Turnbull, Osprey Publishing
  A fascinating and lavishly illustrated guide to the world of the Samurai warrior, delving into the history of their campaigning, their arms and armour, as well as their day-to-day lives and their warrior ethos.
  
  The world of the samurai, the legendary elite warrior cult of old Japan, has for too long been associated solely with military history and has largely remained a mystery. In this exciting book, Stephen Turnbull, the world's leading authority on the samurai, goes beyond the battlefield to paint a picture of the samurai as they really were.
  
  The world of the samurai warrior is revealed to be one of great richness, with familiar topics such as the cult of suicide, ritualised revenge and the lore of the samurai sword being seen in the context of an all-encompassing warrior culture that was expressed through art and poetry as much as through violence.

• A Brief History of the Samurai. Jonathan Clements, Robinson Publishing
  The Samurai emerged as a warrior caste in Medieval Japan and would have a powerful influence on the history and culture of the country for the next 500 years. From a leading expert in Japanese history, this is one of the first full histories of the Samurai warrior

• The Samurai Warrior, The Golden Age of Japan's Elite Warriors 1560-1615. Ben Hubbard, Amber Books
  The Samurai Warrior describes the major battles of the era, the weapons and armour used, the social structure of Japanese society, myths about the samurai, and finally their decline during the modernization of the Meiji period. Including more than 200 photographs, illustrations and maps, it is a colourful, accessible study of Japan s warrior elite.

Here are a few very specific things about the Samurai and the Sengoku Period that some might find interesting. All of these are from Osprey Publishing and all except one, which I added the author to, are by Stephen Turnbull.

• Weapons of the Samurai

• Samurai Armour. Trevor Absolon

• The Samurai and the Sacred

• Samurai Women 1184–1877

• The Samurai Capture a King

• The Samurai Invasion of Korea 1592–98

• Samurai Commanders (Volume 1 and 2)

• Samurai Heraldry

• Katana, the Samurai Sword

• Hatamoto

• Osaka 1615

• Kawanakajima 1553–64

I hope this list is helpful to anyone searching for some literature about the Sengoku Period! I might add more books later. And, like I said, if you know any other books, just comment.

:)