Welcome! I hope you enjoy your agile transition.
Some people think they can transition to agile by absorbing the vocabulary from the “ether.” When I help those people, they discover they are missing key concepts. You will need to read and practice significant changes for your agile transition.
This is a minimum reading list. This is not everything you could read, not at all. This reading list is in addition to my talk, Agile Projects, Programs, and Portfolio: No Air Quotes Required. After the talk, I will post the slides here.
I hope, with the help of readers and commenters, that you will help me add books and articles over time. However, I would like to keep the main page to a minimum reading list. The page does people no good if it's overwhelming.
You should read the Scrum Guide on Scrum.org. However, that's not enough to learn how to use Scrum. (Well, not in my opinion.) Read a Scrum book. There are plenty out there. I read the original Schwaber and Beedle book: Agile Software Development with Scrum (Series in Agile Software Development).
When I first started doing agile, I knew I couldn't do more than one thing at a time. It turns out I did know about kanban, I didn't know the name. David Anderson's Kanban book will tell you more than just the name.
Iterations and increments are not enough. If you don't incorporate the engineering practices and keep your code clean as you develop your features, you will not succeed. You need to do learn how to do this. The (classic) book I have is: Extreme Programming Explained: Embrace Change, 2nd Edition. I have the first edition. Yes, I am linking to the second edition. Let's embrace some change here.
Project Portfolio Management:
One of the problems when you transition to agile is that you must commit to doing one project at a time, with one project team. No multitasking. You can learn to flow work through teams. This is difficult for many managers. My book, Manage Your Project Portfolio: Increase Your Capacity and Finish More Projects explains how.
Mike Cohn's book User Stories Applied: For Agile Software Development is a classic.
I also like George Dinwiddie's handout about how to make user stories smaller.
Mike Cohn has another classic: Agile Estimating and Planning.
I like Ron Jeffries' article Big Visible Charts. You could read everything Ron has to say. If you disagree with him, put aside your disagreement for now, and try what he says for a month or two. Once you've tried it his way, really tried it, and removed all your obstacles so you can try it, then you might have the experience to disagree with him.
Agile Retrospectives: Making Good Teams Great. I wish I had a penny for every time I suggested this book. They really should pay me for this, but they don't. Oh well. If you only get one retrospective book, get this one. It's awesome.
You might consider reading Manage It! Your Guide to Modern, Pragmatic Project Management if you don't know how to charter a project, or if you don't know how to use iterations, or work incrementally. Or, if you don't know how to be a servant leader project manager.
If you want to be a servant leader manager, read Behind Closed Doors: Secrets of Great Management.
If you want to get into the mindset of learning through experimentation, read Eric Ries' The Lean Startup: How Today's Entrepreneurs Use Continuous Innovation to Create Radically Successful Businesses. It's not just for software.
Tobias Mayer has created a terrific resource site that is more than a minimal reading list. See AgileLib.net.
General Notes About My Recommendations
If you have taken training from a trainer, and you have his or her books, terrific. Use their book(s). If you have bought other books, wonderful. I have about 75 or 80 books in my agile library. Yes, my agile library. As I said, this is the minimum reading you should do. If you have other, better books, that is wonderful. There are many other books I wanted to tell you to read.
For example, you could go to the Pragmatic Bookshelf, buy any of the agile books there, and be very happy. No doubt about it. I wanted to point you to the original texts, the ones I read at the start of my agile journey. Is that the right thing? I don't know. I'm working on providing the minimal reading list. As with providing a minimum viable product, (MVP), this is a difficult thing to do.