I made a summary of a book I used in class years ago in order share it with my students. In the summary, I took whole sentences and equations from the original book, and reduce the pages from 600 to 200, my intention at that time was to give to my students a more compacted book which implemented the important information for the class. The mistake I made was to put my name in this summarized book and shared the book with my students. My name is on the cover and in all the pages. Back then, I did not consider this could affect me, but I realized weeks ago that the book was uploaded to the internet through Scribd and SlideShare. I have been extremely preoccupied since then. I fear the editorial of the original book can take legal action against me. Do this can lead to legal problems? The summarized book has been on the internet since 2011, is there the possibility of a demand coming from the editorial or author of the original book?
The basic question is whether you "copied" the book, which is not limited to verbatim cut and paste type copying. Even with verbatim quotes and equations copied from the book, some amount of that is allowed under the fair use doctrine. There is not much (any) clarity in the law when it comes to educational-use quote-copying. However, based on your description, I would not conclude that this work counts as "fair use": but a judge or jury might decide it is, depending on the exact facts.
If you reduce a 600 page book to 200 pages, that sounds like "copying" while creating a derivative work. This would be especially the case if the structure of your book strongly resembled the structure of the original book, and what you did was omit some sentences and reword some sentences. On the other hand if you wrote an independent book on the topic, happened to reflect the original author's ideas, and even copied a small amount of text by way of illustrative quotes, then that resembles an independent creation rather than copying.
There are 4 plus factors recognized in the fair use defense, where the fact-finder would somehow "take into consideration" these factors: purpose and character (non-profit, teaching, exegesis all in your favor), nature of the work (equations implies science hence facts, being factual favors fair use), amount and substantiality (not in your favor, if you're paraphrasing a whole book), and effect on market. As a first approximation, your work might have a devastating effect if your work is good and the original is expensive plus popular – you created a free competitor. Framed in terms of your intended original use, probably not so significant, limited to the size of your class (assuming that your work was a replacement for, and not a supplement to, the original – which may be what you did). The law isn't stated in terms of your intent in creating the work, it's stated in terms of what you did. Still, the fact-finders might be influenced by innocent intent. Then finally, there is "transformativeness" as a unifying consideration, so that copying that substantially transforms a work into a new work fares better under a fair use analysis – this would appear to be a quite transformative work.
Whether or not the rights-holder is likely to go after you depends on many unknowables, especially whether there would be any point in suing you, and how much the publisher and author care.
Regardless of the relationship between the original book and your version, you have created a work that is also protected by copyright. That means that it is illegal to upload your work to Scribd, Slideshare, or anywhere else, without your permission. When someone illegally uploads a work to a server, if you learn about it, you as author can file a DMCA takedown notice. A law-abiding service will then take the work down (unless the uploader officially claims he has the right to upload it). If they do claim they have the right, you have to sue them. So even if it's all over the internet, you can play whack-a-mole with copies and get many of them taken down.