The IX Annual International Scientific Conference "Modern Methods and Problems of Operator Theory and Harmonic Analysis and Their Applications (OTHA-2019)" took place on April 21-26, 2019 at the Southern Federal University. Conference website: http://otha.sfedu.ru/conf2019/ thanks to more than 130 participants from many countries worldwide. The list of plenary speakers: Alexandre Almeida (Portugal), Anatoly Antonevich (Belarus), Oscar Blasco (Spain), Viktor Burenkov (Moscow), Mikhail Goldman (Moscow), Vagif Guliev (Azerbaijan), Alexey Karapetyants (Rostov-on-Don), Kazaros Kazarian (Spain), Vladislav Kravchenko (Mexico and Rostov-on-Don, Russia), Anatoly Kusraev (Vladikavkaz), Elijah Liflyand (Israel), Alexander Mikhailov (Great Britain), Helmuth Malonek (Portugal), Boris Mityagin (USA), Alexander Nazarov (St. Petersburg), Eugeny Panov (Velikiy Novgorod), Boris Plamenevsky (St. Petersburg), Vladimir Protasov (Moscow, Russia and Italy), Armen Sergeev (Moscow), Stefan Samko (Portugal), Natasha Samko (Norway), Yoshihiro Sawano (Japan), Andrei Shkalikov (Moscow), Maria Skopina (St. Petersburg), Alexandre Soldatov (Moscow), Jari Taskinen (Finland), Joachim Toft (Sweden), Sergey Vodopyanov (Novosibirsk). The following sections were organized: Functional Analysis and Operator Theory, Theory of Functions and Approximation Theory, Differential Equations and Mathematical Physics, Probabilistic-Analytical Models and Methods, Bioinformatics and Mathematical Modeling, Hausdorff Operators and Related Topics. Thus, the focus of the conference is fundamental mathematics, but there were also considered problems of applied mathematics. The conference was supported by the Regional Mathematical Center of the Southern Federal University in collaboration with the Institute of Mathematics, Mechanics and Computer Science of the Southern Federal University, and is also supported by grant from the Russian Foundation for Basic Research  and by the ISAAC society.