Professor of Government at Georgetown University in Qatar, Mehran Kamrava, penned one of the most read / taught books on Qatar in 2013 (with a 2015 adding an updated Preface): Qatar: Small State, Big Politics. Having read a few books on Qatar, this is one of the best, although increasingly dated (the content essentially up to 2012). Nonetheless, this is a good primer, and for those interested in the country, worth a read. A few notes:
Context on book: "The emergence of Qatar as an influential powerbroker in the Middle East and beyond over the past decade has puzzled students and observers of the region alike. How can a small stake, with little previous history of diplomatic engagement regionally or globally, have emerged as such an influential and significant player in shaping unfolding events across the Middle East and elsewhere? This is the central question to which this book is devoted." (p. 1)
"Ascendance is not without its risks, and many deep-seated structural limitations impede, or altogether threaten, the meteoric rise of the Middle East's newest heavyweights. I argue that in many ways Qatar is immune to many of these risks and limitations, and, insofar as its international profile and power-projection abilities are concerned, it has therefore been able to stand above the rest of the pack so far. The unique rise of Qatar is facilitated by a combination of factors that are both structural and contextual, in relation to its neighbours, and agency related - that is, its own resources and its employment of those resources and its agendas for purposes of power projection." (p. 18)
"Hedging may be defined as "a behavior in which a country seeks to offset risks by pursuing multiple policy options that are intended to produce mutually counteracting effects, under the situation of high-uncertainties and high-stakes." Hedging stresses engagement and integration mechanisms, on the one hand, and realist-style balancing and external security cooperation, on the other... It is a carefully calibrated policy in which the state takes big bets one way - for example, in Qatar's case opting for the US security umbrella - while it also takes smaller bets the other way, as in maintaining friendly ties with Iran and regional Islamists." (p. 51-52)
"A second, rather distinctive, branding strategy that Qatar employs is through proactive attempts at regional conflict resolution. Over the past decade, Qatar has become one of the world's most active mediators in international conflicts across the Middle East and parts of Africa, and in the process it has actively cultivated an image of itself as an honest broker interested in peace and stability. These have included mediation efforts in Yemen, Palestine, Sudan, Djibouti and Eritrea, and, most notably, in Lebanon." (p. 93) Since the book was written, probably even more notable is the brokering efforts in Afghanistan.