This study is to in-depth analysis of the copyright issues related to the library's e-book service, which is the cause of the recent conflict between the publishing industry and the library industry. To this end, the purpose and outline of the copyright system were briefly summarized. Then, the jurisprudence of the Copyright Act applied to the borrowing of paper books and e-books was analyzed, and the position of the publisher's association and the library industry were reviewed together. In addition, problems of the current copyright act related to e-book services were diagnosed and directions for improvement were sought. Unlike in the case of paper books, first sale doctrine does not apply to e-book borrowing, so the library cannot acquire the right to service just by purchasing e-books. Based on the contract signed with the distributor in the process of purchasing the e-book, the library acquires the right to service the e-book. However, if the validity period of the exclusive publication right expires, the contract itself becomes invalid, which can cause serious problems in the stability of library services and preservation of resources. In order to solve this problem, it is suggested that the first sale doctrine needs to be extended to digital works.