The institute of Mathematics and Mechanics was created in 1959 on the basis of the department of Mathematics of the Institute of Physics and Mathematics of AS of Azerbaijan SSR. (resolution №319 of the council of Ministers of Azerbaijan SSR dates from April 27, 1959 and report №11 of the meeting of the Presidium of Academy of Sciences of Azerbaijan SSR dated from May 6, 1959.)In 1959 the Institute consisted of 5 departments: the departments of theory of functions, differential and integral equations, approximate analysis, theory of elasticity and the computer center. The famous scientists M.V. Keldysh, M.A. Lavrentyev, I.N.Muskheleshvili, I.G.Petrovsky, S.L.Sobolev, Gelfhand, S.N. Bernstein and A.I.Maltsev have played a great role in creation and development of these directions.(The first row from the left: director of the Institute of Mathematics and Mechanics of NASA acad. Zahid Khalilov, prof. Amir Habibzade, prof. Hashim Agayev, the corr. members of the NASA: Goshgar Ahmedov, Yusif Amen-Zadeh, Yahya Mamedov, acad. Faramaz Maksudov, corr. member of the NASA Arif Babayev, acad. Mirabbas Gasymov. The second row from the right: the honoured scientist prof. Melik-Bakhish Babayev, doc. Alif Babayev, Yashar Kerimov, Israil Mehdiyev, prof. Aladdin Mahmudov, the corr. member of NASA Mais Javadov, prof. Yuri Domshlak.)(From the right: decent Almas Huseynbeyova, prof. Shamil Vekilov, corr. member of NASA Bala Iskenderov, docent Khamis Najafov.)(The department of theory of functions: from the left: docent Elman Gasymov, Natig Hajiyev, Kamil Musayev, prof. Daniel Israfilov, the honoured scientist prof. Melik-Bakhish Babayev, acad. Ibrahim Ibrahimov (the head of the department) , Akif Gadjiev, doc: Vaqif Shahverdiyev, Nizami Shykhaliyev, Hidayat Hasanov)THE BASIC SCIENTIFIC DIRECTIONSSPECTRAL THEORY OF OPERATORS AND THEORY OF OPERATOR ALGEBRAS.Department of functional analysis doctor of physico- mathematical sciencs, prof. Hamidulla I.Aslanov.Department of non-harmonic analysis doctor of phys. math. sci. prof. Bilal T. Bilalov.PROBLEMS OF THEORY OF FUNCTIONAL SPACES AND HARMONIC ANALYSIS IN MANIFOLDS.Department of mathematical analysis: doctor of phys. math. sci. prof. Rahim M. Rzayev.Department of theory of functions cand. of phys. math. sci. Vugar E. Ismailov.GENERAL AND QUALITY THEORY OF DIFFERENTIAL OPERATOR EQUATIONS.Department of differential equations doctor of phys. math. sci. Akbar B. Aliyev.Department of mathematical physics equations corr. member of NASA prof. Rauf V. Huseynov.PROBLEMS OF ALGEBRA AND MATHEMATICAL LOGICS: HISTORY OF SCIENCE AND ENGINEERING.Department of alfebra and mathematical logic: cand. of phys. math. sci. Ali A. Babayev.COMPUTER-INFORMATION AIDS FOR SOLVING INTERDISCIPLINARY MATHEMATICAL PROBLEMS.Department of computing mathematics and informatics cand. of phys. math. sci. Fariz B.Imranov.Department of applied mathematics doctor of phys. math. sci. Gabil G. Aliyev.MECHANICS OF DEFORMABLE SOLIDS: UP-TO-DATE PROBLEMS OF NON- LINEAR MECHANICS OF FLUID AND GAS.Department of elasticity and plasticity. doctor of phys. math. sci. prof. Vagif J. Hajiyev.Department of fluid and gas mechanics. acad. of Russion Academy of Technical Sciences doctor of technical sciences Geylani M. Panahov.Department of creeping theory doctor of phys. math. sci. prof. Latif Kh. Talybly.Department of wave mechanics doctor of phys. math.sci. prof. Safar H.Agalarov.The autstanding scientists of the former Sovient Union M.V.Keldysh, I.G.Pertovsky, B.M.Levitan, A.G.Kostyuchenko, A.A.Gonchar, P.L.Ulyanov , Y.M. Berezansky, O.A.Lodyzhenskaya, A.D.Kudravtsev, O.A.Oleynik, Q.E.Shilov, V.A.Il`in, S.N.Bernstein, A.V.Skorokhod. M.A.Naimark, Kh. A. Rahmatulin, A.N.Goose, N.Bogolyubov, S.L.Sobolev, A.N.Tikhonov, D.M.Nikolsky, V.S.Vladimirov and other scientist have played a great role in creation and development of these fields.In the course of 50 years the academician Zahid I. Khaliliv (1959; 1967-1974); acad. Ibrahim I. Ibrahimov (1959-1963); doctor of phys. math. sci. prof. H.M. Agayev; acad. Faramaz G. Magsudov ( 1974-2000) , corr.- member of NASA prof. Ilham T. Mamedov (2000-2003), acad. A. Dj. Gadjiev (2004-2013) were the directors of the Institute of Mathematics and Mechanics. From 2013 the doctor of phys. math. sci. prof. Misir Mardanov is at the head of the Institute.Zahid İ.Xəlilov (1959; 1967-1974) akad. İbrahim İ.İbrahimov (1959-1963) prof. Həşim M.AğayevAcademicianZahid Khalilov AcademicianIbrahim Ibrahimov ProfessorHashim Agayevakad. Fərəməz Q.Maqsudov (1974-2000) AMEA-nın müxbir üzvü, prof. İlham T.Məmmədov (2000-2003)AcademicianFaramaz Maksudov ProfessorIlham Mamedovakad. A.C.Hacıyev (2004-2013) 2013-cü ildən İnstituta f-r.e.d., prof. Misir MərdanovAcademicianAkif Gadjiev ProfessorMisir MardanovThe institute of Mathematics and Mechanics was created in May 1959 and the main goal of its creation was to serve to development of mathematical and mechanical sciences in our country. The main basis of the institute was the mathematical sector of Institute of Physics and Mathematics created in 1945. At that time as in subsequent years collaborators of Azerbaijan State University and Azerbaijan Pedagogical Institute have worked at the Institute of Physics and Mathematics as half-timers and scientific investigations have been carried out in traditional directions of the Republic.In 1950-1957 the outstanding mathematician academician Z.I. Khalilov has been at the head of the Institute of Physics and Mathematics. The first director of the Institute of Mathematics and Mechanics was acad. Z.I.Khalilov the deputy director the candidate of phys. math. sciences H.N.Agayev, the scientific secretary Y.I.Domshlak.The Institute had the following departments and laboratories: the department of functional analysis (the head of the department acad. Z.I.Khalilov) , dep. of functions theory (acad. I. I.Ibrahimov), dep. of differential equations ( cand. of phys. math. sci. H.N. Agayev), dep. of integral equations (cand. of phys. math. sci. Sh.I. Vekilov) dep. of approximate analysis (cand. of phys. math. sci. A.S.Jafarov), dep. of theory of elasticity (doctor of phys. math. sci. Y.A. Amenzadeh), laboratory of dynamical strength (cand. of phys. math. sci. K. A. Kerimov) and computer center ( cand. of phys. math.sci. S.A.Aleskerov).It should be especially noted that the heads of two department on mathematics Zahid Ismayil oglu Khalilov and Ibrahim Ibish oglu Ibrahimov and the heads of the departments and laboratory on mechanics Yusif Amen oglu Amenzadeh and Kerim Abdulkhalig oglu Kerimov were the outstanding scientists that laid the foundation of these fields in our country.From 1960 the computer center parts from the Institute and functions as an independent computer center. After some times the Institute of Cybernetics of the Academy is created on the basis of this center. So, by creating the IMM, 3 of its collaborators were the doctors of physico mathematical sciences (one academician, one corresponding member) and one the main goals of the institute was to prepare the doctors on different fields of mathematics and mechanics.The first director of the Institute acad. Zahid Khalilov was an outstanding scientist that had indispensable services in creation and development of the school of functional analysis in our country was the founder and leader of this school to the end of his life. After graduating from Azerbaijan State Pedagogical Institute Zahid Khalilov works as a docent in Tbilisi at the Institute of Railway transport engineers. In 1937 he becomes a post graduate student of the famous mechanical engineer, after words the academic secretary of the AS of the USSR N.Z.Muskheleshvili and after earning his candidate degree he comes back to Baku and becomes a docent at Azerbaijan State University. In 1942 he works at the sector of physics of Azerbaijan branch of the AS of the USSR and that time he was the first and only mathematician of this sector. Then in 1945 the Institute of Physics-mathematics is created on the basis of this sector. In 1946 Zahid Khalilov earns his Doctor degree and becomes the first doctor on mathematics in Azerbaijan.Zahid Khalilov was one of the first Soviet scientists that felt the great importance of functional analysis, functional methods in theory of differential and integral equations. This book “the fundamentals of functional analysis” is the first book devoted to functional analysis in the USSR. He is also one of the first scientists in the USSR that has investiged differential equations in the classes of Banach-valued functions. In 1955 Zahid Khalilov was choosen an academician. In 1957-1959 he was the vice-president of the Academy of Sciences, in 1957-1962 the academic secretary of the department of physical mathematical technical sciences, 1957-1967 the president of the Academy of Sciences, from 1967 to the end of his life, i.e to 1974 he was the director of IMM.In 1959-1963 the Director of the IMM was the founder of the school of theory of functions in Azerbaijan, the leader of this school to the end of his life, the outstanding mathematician academician Ibrahim Ibish oglu Ibrahimov.After graduating from Azerbaijan State Pedogogical Institute, I. Ibrahimov beging to work at API and at Azerbaijan State University. Then he was sent to Moscow post-graduate courses and became a student of the famous mathematician A.O. Gelphand. In 1939 he earns his cand. degree and becomes the first candidate of sciences in Azerbaijan. In 1947 he earns his Doctor’s degree in Moscow. I. Ibrahimov was our scientist recognized by the mathematicians of the Soviet Union and the world. He has supervised some investigations on theory of approximation of a real and complex variable functions, theory of interpolation, theory of entire functions, the completeness of the system of functions and great majority of these investigations have found their reflection in his books published in Moscow as well. The papers written in colloboration with the outstanding scientists of our time M.V. Keldysh and A.O.Gelphand have put great traces in references on mathematics. The report made by him at the International Conference dedicated to one of the creators of construction theory of functions academician S.N. Bernstein is the index of his authority. In 1959 I.Ibarahimov was selected a corr.- member of the Academy, in 1968 an academician.In 1963-1967 prof. Hashim Agayev was an acting director of the IMM.1967-1974 Z.Khalilov again was at the head of the Institute.1974-2000 the director of the Institute has been Faramaz Gazanfar oglu Maksudov.In these years there was a great raamination in preparation of doctors at the Institute. Though in 1959-1974 3 doctor’s degrees were defended at the Institute, at subesequent 15 years 15 Doctor’s degrees were earned (9 of them on mechanics). This was the result of tireless activity of Faramaz Maksudov. He succeeded in getting the young scientists to be known at the most advanced scientific centers of the USSR .In 1976 Faramaz Maksudov was elected a corr. member of the Academy, in 1980 an academician. Till the end of his life he was the Director of IMM and at the same time in 1980-1997 he was the academician-secretary of the department of physico- mathematical technical sciences of the Academy, in 1997-2000 the President of the Academy.From 2003 to 2004 the director of the Institute was the talanted mathematician Ilham Mamedov that has earned his candidate of sciences and doctor’s degrees when he was too young.In 2001 he was selected a corr. member of the Academy. Ilham Mamedov was a known specialist in quality theory of differential equations, an author of monumental scientific papers and supervisor of a lot of candidates of sciences.From 2004 to May 2013, acad. honoured scientist, doctor of phys. math. sci. Professor Akif Gadjiev has been at the head of IMM.At the same time since 2001 he is the academic-secretary of department of physico- mathematical sciences of NASA and since may, 2013 the vise-president of the Academy of Sciences.From may 2013 the doctor of physico-mathemtical sciences professor Misir Mardanov is at the head of the Institute.