Mr. Casaubon spends a lot of time at Tipton Grange during the period leading up to their marriage. He doesn't enjoy it, though – it's time taken away from his scholarly work.
Dorothea, meanwhile, is eager to prepare herself for her duties as Mrs. Casaubon. She asks him whether she should start learning Greek or Latin, in order that she might better be able to help him with his work. Learning Latin and Greek sure is fun (no, seriously!), but Dorothea might not have the best reasons.
Mr. Brooke isn't sure that learning Latin or Greek will be good for her – female minds being weak and all that.
He thinks women should stick to music and light reading.
Mr. Casaubon doesn't like music much, anyway – he's happy for Dorothea to learn to copy Greek characters so that she'll be able to copy manuscripts for him, and save his eyes.