Translation:I am taking the big book with me.
"Bring" is "alkondukas". The difference between take and bring is like the difference between go and come which all comes from the speaker's point of view. I am leaving when I take something with me and I am coming when I bring something with me. http://www.gutenberg.org/files/16967/16967-h/16967-h.htm#letterB
Isn't the difference between "take" and "bring" direction? If I am going away from you, I am "taking", if I'm coming toward you, I am "bringing". E.g. I am taking the book with me = I am at your house and I am leaving and the book is with me. / I am bringing the book with me = I am at my house and I'm coming over to your house and I have the book with me. In Hungarian, there's a difference between "take with me" (viszem magammal) and "bring with me" (hozom magammal).