Twitter is a social networking platform that has become popular in recent years. It has become a versatile information dissemination tool used by individuals, businesses, celebrities, and news organizations. It allows users to share messages called tweets with one another. These messages can contain different types of information from personal opinions of users, advertisement of products belonging to all kinds of businesses to the news. Tweets can also contain messages that are racist, bigotry, offensive, and of extremist views as shown by research. Manual identification of such tweets is impossible as hundreds of millions of tweets are posted every day and hence a solution to automate the identification of these types of tweets through classification is required for the Twitter administrators or an intelligence and security analyst. This paper presents a comparative study of traditional machine learning algorithms and deep learning algorithms for the task of tweet classification to detect different categories of abusive languages with the aim to determine which algorithm performs best in detecting abusive language that is prevalent on social media. Two approaches for building feature vectors were explored. Feature vectors based on the bag-of-words method and feature vectors based on word embeddings. These two methods of feature representation were evaluated in this paper using tweet messages representing five abusive language categories. The experiments show that the deep learning algorithms trained with word embeddings outperformed all the other machine learning algorithms that were trained with feature vectors based on the bag-of-words approach.