The browser is the way users interact with the internet and for frontend developers it is important to pick a browser that you like, you will spend a lot of time working in it.
The rest of this document will assume that you are using chrome.
Developer tools are provided to you by the browser and you will use them every day.
You can read more about developer tools here.
The DOM is what the browser creates from the html on the page and it is what you use to interact with the browser from JavaScript.
You can read more about the DOM here.
Cookies are a way for developers to store information in the users browser and they are a vital part of making web applications.
You can read more about cookies here.