Teaching styles play a crucial role in teaching language skills. Teaching Reading Comprehension and Essay Writing are not exceptional. The educational system is based on three main correlated pillars, namely the instructor, the students, and the subject/teaching material. Focusing on one pillar on the account of the other two may destabilize the educational system. As such, do instructors teaching styles correlate with students achievement? On this basis, the current research aims at investigating the correlation between the teaching styles (TSs) of instructors of English as a foreign language (EFL) and male and female students' academic achievement in the subjects of Reading Comprehension and Essay Writing at university level. It hypothesizes that there is no correlation between teachers teaching styles and students academic achievement. The selected sample comprised 6 instructors and 1339 second and third-years students of the Departments of English language at the College of Education and College of Basic Education / University of Mosul. Concerning students' academic achievement, the researchers considered the scores of the term exam in the researched teaching subjects for the sample of students of the College of Education and the scores of the semester final exam for the sample of students of the College of Basic Education. Staffordshire Evaluation of Teaching Styles Questionnaire was used as a tool to identify instructors' teaching styles. The results demonstrated that the level of correlation between instructors teaching styles and students academic achievement range from moderate to very strong, i.e. the correlation is positive. Moreover, the level of correlation between instructors teaching styles and students academic achievement in Reading Comprehension is 0.8118 compared to 0.8178 in Essay Writing. As a general conclusion, it has been noticed that all the researched teaching styles have a positive impact on students achievement in general, and in RC and EW in particular. Finally, some suggestions for future research have been forwarded.