Redmine

I've read through many pages of the user guide how to and FAQ

Before I pay for hosting and have this set up ai have one vital question

If i have more then one project

Project A
Project B

Can users be set up so that for example

david - sees project a and b
ashley - sees project a and has absolutely no access to even see project b or know of it's existense

i'm looking for one red mine set up, many projects, many users and users can only see the project they're involved in. or do i need to set up multiple redmine areas? can someone direct me to correct documentation or give me an easy answer?