The Law overrode everything else – personal need, grief, loss, unfairness, treachery. When the Clave had told Emma that she was to accept the fact that her parents had been murdered as part of the Dark War, she had been required to do so. She hadn't.”
-- Narrator (Chapter 1, A Sepulchre in This Kingdom)

Importance: This is the first look at the power of the Clave, which is the government of the Shadowhunters, and the fact that they consider themselves unimpeachable. Emma learns that her parents were not murdered as part of the Dark War. Her refusal to do so shows her individuality.

Sometimes it was hard not to feel bitter, Julian reflected, that all the allies and friends in his life were either people he had to lie to, ridiculous, or both.”
-- Narrator (Chapter 4, And This Was the Reason)

Importance: Julian says “all” the people in his life, which apparently includes Emma. He will soon reveal that he is basically running the Institute because Arthur is not...