Order of Pheonix
In the beginning, two Dementors show up in the town of Little Whinging and attack Harry and his cousin, Dudley. When Harry uses magic to drive them off, however, he quickly receives a succession of owls from the Ministry, requiring him to attend a disciplinary hearing. His heart sinks when he reads that the question of whether to expel him from Hogwarts will be decided at the hearing.
Harry is exonerated at the hearing but when Harry finally manages to make it back to school, he finds things are different than when he left. Hagrid's not there, there are skeletal horses pulling the school carriages that only he can see, and the new Defense Against the Dark Arts teacher is none other than toadlike, repulsive Dolores Umbridge, a Ministry representative whom Harry is all too familiar with.
Nobody believes Harry or Dumbledore when the say Voldemort has retuned.As the school year progresses Harry and Umbridge makes it really hard for Harry, she retaliates by taking away everything he cares about: Quidditch, letters from Sirius, and visits with Hagrid. So Harry fights back the only way he can, by forming a secret defense group, known as Dumbledore's Army, and teaching his friends how to fight properly.
In spite of the frantic workload in preparing for their OWLs (tests that determine the student's future career choices), the tyranny of Umbridge, and Harry's unbearable crush on Ravenclaw seeker, Cho Chang, Harry keeps having tantalizing dreams of dark corridors and locked doors that are distracting at best. His scar prickles constantly and he soon finds he's turned into a tiny antenna for Voldemort's mood swings, which certainly doesn't help his own temper.
Things take a disastrous turn when Dolores Umbridge finds out about Harry's secret defense group. Harry is filled with guilt when Dumbledore, claims credit for the group in order to protect Harry, and has to flee the school to escape arrest.
This installment ends with an epic battle of good and evil, resulting in a devastating loss to Harry when his godfather Sirius Black is killed, and the full revelation that his destiny lies intertwined with none other than Voldemort himself. In the end, Dumbledore reveals the lost prophecy to Harry: either Harry will kill Lord Voldemort or Voldemort will kill Harry.
Half Blood Prince
Harry's sixth year at Hogwarts opens to find him more mellow and grown up than ever. The death of Sirius Black has left an indelible mark on him, and he's more determined than ever to put an end to Voldemort and his Death Eaters. He's happy to escape the tyranny of the Dursley's early in the summer when Dumbledore picks him up to attend to a mysterious errand, which ends up in Harry's persuading ex-professor, Horace Slughorn, to come out of retirement to teach at Hogwarts again.
When the day finally arrives, Harry is as usual overjoyed to be back at school. He's been made Quidditch Team Captain. However, Harry and his friends are dismayed to find out that Professor Severus Snape has finally achieved his burning desire to become Defense Against the Dark Arts professor. Harry is excited to be taking private lessons with Dumbledore this year, who is showing him all about Voldemort's past. Dumbledore hopes that knowing as much as he can about Voldemort will help Harry in his final battle with the Dark Lord.
He finds a book in potions class which belonged to thew Half Blood Prince and starts relying on it too much.
Harry also keeps an increasingly close eye on Draco Malfoy. Convinced that Malfoy has replaced his father as the head of the Death Eaters, Harry believes Malfoy is constructing a dark plot inside the school but can't for the life of him figure out what it is. Between Ron and Hermione's skepticism, and Malfoy's disappearances from the school grounds, Harry has his hands full trying to uncover what Malfoy's up to.
His lessons with Dumbledore continue sporadically, and he's excited to hear that he might be able to go with Dumbledore on a dangerous mission to help destroy a horcrux that contains a part of Voldemort's soul. Together they go on an adventure to find the horcruxes and when they return to Hogwarts they see the Dark Mark over the castle which ends in a big fight.
Hope this helped!