Definition:
hope is a noun which can refer to a feeling of trust in a good outcome and/or a desire for something to happen. It can be used in both countable and uncountable ways. When used uncountably, it means general optimism; when used countably, it implies a specific desire or goal.
Examples:
1. She expressed hope that the project would be successful.
2. He offers hope to those in need.
3. She has no hope of succeeding.
Definition:
hope is also a verb, meaning to feel or express optimism about something. When we hope, wepostulate that a certain thing will happen, although these desires have not necessarily been assured of coming to fruition.
Examples:
1. They all hoped for a better future.
2. I hope that this excitement will last.
3. She hopes to study abroad next year.
Tips:
as a verb, hope is ussually followed by a that-clause, which implies the desired outcome.