“Me” is a pronoun that connects or drivers the verb object to the first person singular. Give me this book – Dê-me este livro. (Formal)/Me de este livro (Informal*). Paulo told me that... Paulo me disse que.../Paulo disse-me que.. I like this book… - Me too. Eu gosto deste livro.. -Eu também*. “Mim” is a form of first person singular pronoun “Eu”, it is used when the action verb requires a preposition. Therefore, you cannot start a sentence with “Mim”. Give this book to me – Dê este livro a mim/Dê este livro para mim. (Prepositions “a” and “para”) Came with me – Venha comigo. In this case, preposition “com” + the pronoun “mim” = comigo. This is a very nice source about Portuguese pronouns, look: http://www.filologia.org.br/anais/anais%20iv/civ01_53-60.html (In Portuguese) *Another site about the correct position of the pronoun http://www.ciberduvidas.pt/pergunta.php?id=12342 (Also in Portuguese) Both works for general Portuguese language, including Brazilian.

"Me" is almost like "para mim" or "em mim" (with prepositions). ex 1: "Me dê o lápis, por favor." (Give me the pencil, please.) ex 2: "Dê o lápis para mim, por favor." (Give the pencil to me, please.)