Michael Charney's {{A History of Modern Burma}} describes the country's major events starting with its integration into British Empire in 1886 through its people's struggle for liberation and decades of political instability up to destruction of its southern part by Cyclone Nargis in 2008. Robert Taylor's {{State in Myanmar}} depicts the relationship between states, both monarchical and morden, and society in the country. Arthur Phayer's ((History of Burma)) is also a classic although it is heavily relied on royal chronicles written in early 19th century. Books written by Thant Myint U are also worth reading. You should accompany them with John F. Cady's {{The Making of Modern Burma}}.
If you want to know about the civil wars raging the country since it obtained its independence from the British in 1948, Bertil Lintner's {{Burma in Revolt}} is a good place to start. Lintner's {{Outrage}} describes 1988 uprising, a major turning point in country's history. {{Caretaking Democratisation}} could make you understand country's political developments between 2010-2016 (Unfortunately, I forgot the author's name on this one).