build up

build a better mousetrap

To create a new product, method, or idea that is better than an existing version of something already common or widely used.

build a case

to compile evidence that supports a charge against someone.

build bridges

Often followed by between or to: to establish friendly relations or links.

build castles in the air

To have any desire, idea, or plan that is unlikely to be realized; to imagine visionary projects or schemes; to have an idle fancy or a pipe dream; to daydream.

build character

To improve a person's character by developing personality traits such as resilience or responsibility.

build on sand

To put something in an unstable position by failing to give it a secure foundation.

build the plane while flying it

To develop one's approach or strategy to a project while carrying out that project, and not beforehand.