The tetralogy (I learned that word recently; it means a four-part story) began on June 29th with Richard II.
I just finished watching it. It doesn't actually air in the U.S. until January, so I found a link, let it load and plopped myself down. C'est la vie.
Henry IV Parts 1 & 2 and Henry V follow in the successive weeks. The plays are based on three historical kings of England: Richard II, who was deposed by his cousin Henry Bolingbroke, who became Henry IV. Then Henry IV found it hard to keep control of his nobles and his kingdom, including his errant son. That son became Henry V, England's great warrior king, who won a decisive battle at Agincourt against the French.
Here's the trailer for the series, which is being called The Hollow Crown after a speech in Richard II.
Edited to add: A podcast interview with the director, producer and Ben Whishaw and Rory Kinner.
I've had my struggles with Shakespeare in the past. I'm not a poetry person, so I find verse to be a struggle sometimes. As beautiful as Shakespeare's language and poetry are, it's not easy to grasp upon first sight. I think he's a genius, though, but it does need to be made interesting rather than worthy.
I always think Shakespeare is easier to understand when it's being performed in some way. They're plays, after all. I always truly admire actors who can handle the language and make it seem so natural, even when all their dialogue rhymes.