This is the 8421st most frequent Russian word.
надеждой
The Russian word "надеждой" means "with hope" in English.
Here, 'надеждой' is the instrumental case of the noun 'надежда' (hope), and it describes the emotion or attitude with which the subject views the future.
Он смотрел в будущее с надеждой.
He looked into the future with hope.
In this sentence, 'надеждой' is used to express the motivating emotion (hope) that accompanies the subject's actions.
Она работала с надеждой на успех.
She worked with hope for success.
The phrase 'с надеждой' illustrates the idea of beginning something while being filled with the feeling of hope.