This book is the first volume of proceedings from the joint conference X International Symposium "Quantum Theory and Symmetries" (QTS-X) and XII International Workshop "Lie Theory and Its Applications in Physics" (LT-XII), held on 19-25 June 2017 in Varna, Bulgaria.

PART 1: Plenary Talks, Toshiyuki Kobayashi and Alex Leontiev, Image of Conformally Covariant, Symmetry Breaking Operators for Rp;q.- Anthony Joseph, Trails for Minuscule Modules and Dual Kashiwara Functions for the B(¥) Crystal.- Ivan Todorov, From Euler's Play with Infinite Series to the Anomalous Magnetic Moment.- Tamar Friedmann, On the Derivation of the Wallis Formula for p in the 17th and 21st Centuries.- Ivan Dimitrijevic, Branko Dragovich, Zoran Rakic, Jelena Stankovic, Variations of Infinite Derivative Modified Gravity.- Malte Henkel and Stoimen Stoimenov, Infinite-Dimensional Metaconformal Symmetries: 1D Diffusion-Limited Erosion and Ballistic Transport in (1+2) Dimensions.- A.P. Isaev, M.A. Podoinitsyn, Behrends-Fronsdal Spin Projection Operator in Space-Time with Arbitrary Dimension.- Takeo Kojima, Wakimoto Realization of the Quantum Affine Superalgebra Uq(bsl(MjN)).- N.I. Stoilova, J. Thierry-Mieg, J. Van der Jeugt, On Superdimensions of Some Infinite-Dimensional Irreducible Representations of osp(mjn).- G. Manolakos, G. Zoupanos, Non-commutativity in Unified Theories and Gravity.- PART 2: Representation Theory, Jean-Emile Bourgine, Webs of Quantum Algebra Representations in 5d N = 1 Super Yang-Mills.- Patrick Moylan, Parallelizations for Induced Representations of SO0(2,q).- Takuya Matsumoto, Screening Operators for the Lattice Vertex Operator Algebras of Type A1 at Positive Rational Level.- Hendrik De Bie, Roy Oste, Joris Van der Jeugt, Symmetries of the S3 Dirac-Dunkl Operator.- PART 3: Integrability, Natig M. Atakishiyev, George S. Pogosyan, Cristina Salto-Alegre, Kurt Bernardo Wolf, Alexander Yakhno, The Superintegrable Zernike System.- Iana I. Anguelova, The Two Bosonizations of the CKP Hierarchy: Bicharacter Construction and Vacuum Expectation Values.- A.R. Aguirre, J.F. Gomes, A.L. Retore, N.I. Spano, A.H. Zimerman, Recursion Operator and B¿acklund Transformation for Super mKdV Hierarchy.- Kyriakos Charalambous and Christodoulos Sophocleous, Lie Symmetry Analysis of a Third-Order Equation Arising from a General Class of Lotka-Volterra Chains.- PART 4: Entanglement, Hichem Eleuch, Michael Hilke, Richard MacKenzie, Probing Anderson Localization Using the Dynamics of a Qubit.- Mike Hewitt, Pure Spinors, Impure Spinors and Quantum Mechanics.- H. Dimov, S. Mladenov, R. Rashkov, T. Vetsov, Higher-Derivative Oscillators in AdS5£S5 T-dual Penrose Limits.- PART 5: Quantum Groups and Related Structures, A¿ ngel Ballesteros, Rutwig Campoamor-Stursberg, Eduardo Fernändez-Saiz, Francisco J. Herranz, Javier de Lucas, A Unified Approach to Poisson-Hopf Deformations of Lie-Hamilton Systems Based on sl(2).- Huafeng Zhang, Two-Parameter Quantum General Linear Supergroups.- Doman Takata, Noncommutative Geometry and an Index Theory Of Infinite-Dimensional Manifolds.- PART 6: Various Mathematical Results, Cristian Anghel, A Stable Version of Terao Conjecture.-J.F. Colombeau, J. Aragona, P. Catuogno, S.O. Juriaans, Ch. Olivera, Multiplication of Distributions and Nonperturbative Calculations of Transition Probabilities.- Alexander Ganchev, About Markov, Gibbs, ... Gauge Theory ... Finance.- Rosa M. Navarro and Jos¿e M. S¿anchez, A Method for Classifying Filiform Lie Superalgebras.- Maryna Nesterenko and Severin Po¿sta, Equivalence of Vector Field Realizations of Lie Algebras from the Lie Group Point of View.- List of Participants.