This book presents cutting-edge research, advanced techniques, and practical applications of Algebra Analysis and Topology. It offers in-depth insights, theoretical developments, and practical applications, showcasing the richness and interdisciplinary nature of algebra, analysis, and topology. The book fosters a deeper understanding of the fundamental principles while also highlighting the latest advancements and emerging trends in these disciplines. Readers are encouraged to apply the theoretical concepts and techniques to solve mathematical problems, engaging with the book's problem-solving approach. By combining theoretical foundations, practical applications, and interdisciplinary perspectives, this book aims to inspire new avenues of research and contribute to the ongoing development of these dynamic fields.

• Provides a comprehensive and accessible resource that covers a broad range of topics in algebra, analysis, and topology, understanding of the interconnections between these mathematical fields

• Encompasses both classical topics and cutting-edge research areas within algebra, analysis, and topology

• Covers foundational concepts, advanced theories, and their applications in diverse fields such as physics, computer science, engineering, and economics

• Offers sophisticated tools and methodologies to tackle complex problems and deepen the understanding of these disciplines

• Explores how algebra, analysis, and topology intersect with other fields of mathematics and how their concepts and techniques can be applied in related disciplines

It serves as a valuable reference for graduate students, researchers, and mathematicians seeking to deepen their knowledge and engage with the latest advancements in these fundamental branches of mathematics.

Dr. Sandeep Singh is an Assistant Professor with the Department of Mathematics at Akal University Talwandi Sabo, Bathinda, Punjab, India. He received his Ph.D. in Group Theory (Mathematics) from School of Mathematics, Thapar University, Patiala, India and M.Sc. degree in Mathematics from Punjabi University, Patiala, India. He was also a postdoctoral fellow at Department of Mathematics, Indian Institute of Technology Roorkee under programme SERB- NPDF (National Postdoctoral fellowship). His research interests include Group Theory, Automorphism Groups, Number Theory, Sum-set Problems, and Optimization Techniques. Besides holding an excellent academic record throughout, He has cleared the national level examinations NET- JRF conducted by UGC-CSIR, India. Also, He had been a recipient of CSIR junior and senior research fellowship for 2011-2013, 2013-16 respectively. He has published more than 20 research papers in various journals of international repute and of different publishers. He has presented his research work at various international conferences and is the recipient of travel support by the Department of Science and Technology (DST), India. He has a teaching experience of around 08 years. He taught real analysis, ordinary differential equation, linear algebra etc. at UG level and topics in algebra, optimization techniques, probability and statistics at PG Level. He has supervised more than 03 students for their M.Sc. dissertation work and currently supervising 02 Master's students at Akal University. He has also supervised 02 Ph.D. students and presently, 02 students are pursuing their Ph.D. under his supervision. He is a life member of Ramanujan Mathematical Society and Indian mathematical Society and reviewer of American Mathematical Society.

Prof. Kalyan Chakraborty holds a D. Phil. in Mathematics from the Harish-Chandra Research Institute. He is currently serving as a Professor H, Department of Mathematics Harish-Chandra Research Institute, India. His research prowess is evidenced by the publication of more than 58 research papers in prestigious journals, as well as contributions to book chapters and conference proceedings. Under his guidance, 06 Ph.D. scholars have completed their research, while currently, 05 Ph.D. scholars are actively pursuing their studies. Additionally, he has mentored 04 Postdoctoral students, who continue to benefit from his mentorship. Prof. Chakraborty's wide-ranging research encompasses various topics in Number Theory, including the average behaviour of arithmetical functions, Hecke eigenforms, Jacobi forms of higher degree, modular forms, cubic equations in quadratic fields, and the number of real quadratic fields with class numbers divisible by 3.

Dr. Baljinder Kour is an Assistant Professor of Mathematics in the Department of Mathematics, Akal University, Talwandi Sabo, Bathinda, Punjab, India. She obtained her PhD. Degree in Applied Mathematics from the Central University of Punjab, Bathinda, India in 2021. She has cracked national level Lectureship and Junior research fellowship exam three times with all india rank 12, 32, 62 in 2015 and 2016. She graduated with MSc. Mathematics from Kurukshetra University in 2013. She obtained B.Ed. Educational Administration, from Kurukshetra University in 2014. Dr. Kour serves as Reviewer of International Accredited Journals and serves as an editorial board member of peer reviewed journals. She has participated in many international conferences and workshops. She has been supervising Masters degrees students in her university. She has twelve publications in referenced journals and two book chapters to her credit. She has a total of 69 google citations and 5 h-index for the past five years. Her research interests are Mathematical Modelling in educational issues, fractional calculus, symmetry analysis, real analysis and operator theory.

Dr. Sandeep Kaur is currently working as an Assistant Professor at Akal University, Talwandi Sabo, India. He has cleared the national level examinations NET-JRF conducted by UGC-CSIR (2010) and GATE (2011), India. He has also received CSIR junior and senior research fellowship for 2011-2014, 2014-15, respectively. He completed his Ph.D. from Department of Mathematics, Punjabi University, Patiala, under the guidance of Prof. (Dr.) Navpreet Singh Noorie. He has a teaching experience of ten semesters (Aug 2016- June 2022) in Central University of Punjab, Bathinda, India. He is also working on a project funded by TÜBİTAK-BİDEB, Turkey (2022). He has published my research in various international journals and a book chapter in “INSAC Academic Studies on Natural and Engineering Sciences”. Dr. Kaur’s research interests include General Topology, Fuzzy logic & Fuzzy set thoryH and Soft Set theory. He has supervised 27 students of M.Sc. Mathematics and M.Sc. Statistics for their project work in Central University of Punjab, Bathinda, India and delivered three seminars (offline) in Igdir University, Turkey on Induced mappings in Fuzzy and Soft Set theory and their applications. He has attended various ATM Schools workshops organized jointly by TIFR and IIT Bombay, India, and has presented my research in various international conferences.