This show marks the start of Gregory Doran's six-year plan to present the entire Shakespeare canon. It's fair to say that his own beautifully crafted, richly detailed production sets a high standard for himself and others to aim at. David Tennant, in a mesmerising performance that grows in power as Richard's authority declines, also reminds us that the Royal Shakespeare Company is an ensemble that paradoxically needs stars.

It's a sign of Doran's care that he makes clear the complex back-story that illuminates Shakespeare's play. An audience needs to know that Richard's original sin lies in sanctioning the murder of his uncle, the Duke of Gloucester. Michael Boyd began his 2007 production by having Richard stepping lightly over the corpse of the dead duke. Doran, even before Richard's entry, shows us elaborate funeral rites with three sopranos singing religious anthems in the upper galleries and the Duchess of Gloucester bent in grief over her husband's tomb. This is clearly a court steeped in mourning.

The prelude also gives Tennant a vital context in which to work. His Richard, with his brocade gown and Christ-like hair, initially affects an air of listless boredom as his burly barons hurl accusations of treason at each other. But there's a thrilling moment when Tennant gives the banished Mowbray a piercing stare as if daring him to spill the beans about the king's part in Gloucester's murder. Tennant combines inner guilt with a careless disregard for realpolitik as he seizes the land and goods of John of Gaunt after his death: a point reinforced here by the fact that we see tuns of treasure being bodily transported.

Tennant's strengths, as we know from his Hamlet, are a capacity for quicksilver thought and an almost boyish vulnerability. And, even if he might do more to convey the patterned lyricism of the language, what he brings out excellently is the fact that Richard only learns to value kingship after he has lost it. In his decline, Tennant casually tosses the crown away and, at one point, skittishly places it on the head of his adored Aumerle. But in the Westminster deposition scene, where Tennant is at his best, he challenges Bolingbroke to "seize the crown" and, when his rival rises to the bait, immediately inverts it to suggest a falling bucket. Tennant's great achievement is to attract our sympathy to what the gardener calls a "wasteful king" who abuses power when he has it and who achieves tragic dignity only in his downfall.

But this production, which combines period costumes with back-projections in Stephen Brimson Lewis's elegant design, is emphatically no one-man show. Nigel Lindsay's Bolingbroke is a palpably dangerous figure who treats Richard's remission of his initial banishment with surly disdain and openly scorns the deposed king's self-conscious theatricality. It is also good to see a number of RSC veterans operating at top form in key roles.

Oliver Ford Davies is brilliant as the Duke of York in that he highlights both the comedy and pathos of a man torn between ancestral loyalty to the crown and a recognition of Bolingbroke's power. Michael Pennington's John of Gaunt is also a fine study of a dying man bursting with intemperate rage at Richard's betrayal of his country. And Jane Lapotaire turns the Duchess of Gloucester into a silver-haired figure whose widowed grief manifests itself in a burning appetite for revenge.

The packed houses for this production's run in both Stratford and at the Barbican may have much to do with Tennant's star presence. But this is the strongest company the RSC has fielded in years, and what Doran's production brings out is the rich complexity of a play that raises the eternal question of at what point it becomes legitimate to unseat a manifestly flawed ruler. Shakespeare's play may be set in 14th-century England. It remains, however, a timelessly political work.

• Win a pair of tickets to see Richard II on 12 November. For more, go to theguardian.com/extra