The Spartan Constitution or Constitution of the Lacedaemonians (Greek: Λακεδαιμονίων Πολιτεία, Latin: De republica Lacedaemoniorum) by Xenophon is the most comprehensive extant account of Spartan institutions. As an oligarchically-inclined exile from Athens, who had fought alongside Spartan generals in the Persian Expedition, and later against Athens at the battle of Coronea, Xenophon was a well-placed and highly sympathetic observer of Spartan customs.
Free online texts
Gutenberg: The Polity of the Athenians and the Lacedaemonians by Xenophon. Multiple formats.
Loebulus: L183 - Xenophon -- Scripta Minora: Hiero. Agesilaus. Constitution of the Lacedaemonians. Ways and Means. Cavalry Commander. Art of Horsemanship. On Hunting. Constitution of the Athenians. PDF of public domain Loeb edition in Greek and English. Also available from the Internet Archive.
University of Adelaide (Internet Archive): The Polity of the Athenians and the Lacedaemonians by Xenophon, translated by H.G. Dakyns. EPUB, HTML and MOBI formats.
Wikisource: Λακεδαιμονίων Πολιτεία - Greek text. Multiple formats.
BBC Radio 4 In Our Time: Xenophon. Melvyn Bragg with Paul Cartledge, Edith Hall and Simon Goldhill.
Internet Encyclopedia of Philosophy: Xenophon.
Leo Strauss Center: Xenophon, Winter 1963 - audio of lectures on works including The Spartan Constitution.
Further reading at Tom's Learning Notes
Aristotle: The Politics, The Athenian Constitution
Plutarch: Parallel Lives - includes lives of a number of Spartan statesmen: Lycurgus, Lysander, Agesilaus, Agis and Cleomenes.
Ancient Greek resources: Learn to read Greek classics in the original.