What is the main problem in the book?

As this book is a compilation of Eliza's diary entries, the main conflict is the inner conflict Eliza felt as she pursued her intellectual and spiritual growth.

Her journal, while it exhibits an intense earnestness in analyzing the state of her own mind, and perhaps rather too much proneness to dwell morbidly upon it, also evinces the tender joy and peace with which she was often blessed by the manifested presence of her Lord. It unfolds an advancement in Christian experience to which her conduct bore living testimony, and proves that in humble reliance on the hope set before her in the gospel, with growing distrust of herself, her faith increased in God her Saviour, and through his grace she was enabled to maintain the struggle with her soul's enemies, following on to know the Lord.