Perhaps this will be an unpopular sentiment, but I think that you might do well to consider whether this email is a scam of a sort even if it comes from the real Springer publishing company.
Suppose you write this book for Springer. How many copies would it sell? How much will Springer charge for it? Given the answers to these questions, will you make any money? (Short answer: any royalties you do receive will not remotely compensate you for your time.)
So what is your interest in writing such a book? Presumably, getting your ideas out there to the world. This brings me back to the first questions. What does Springer charge for an academic monograph? You might start at their shop website to get a sense of what they charge for similar works. (Short answer: usually >$100 for anything I want, and let's not even get started on the handbooks. Some of these sell for thousands of dollars--for a book!!!) So given these prices, how many copies do you think you will sell? (This is a perfectly fair question to ask the editor who contacted you, but be sure to ask for hard data about comparable books, not an off-the-cuff guestimate.) Are university libraries the primary market, or do they sell an appreciable number of copies to private individuals? How many university libraries have enough money left over from their Springer (and Elsevier, and Wiley, etc) subscriptions that they would buy this monograph. (Conjecture: probably only double figures in the US).
So now imagine that you write this book. Suppose it takes you a year of work (hint: this is a massive underestimate) and you receive close to zero financial compensation. Copies end up in at most a few hundred academic libraries around the world. Was this an efficient way to get your ideas out? Or is this not so very different from any of the other predatory publishers spamming academic authors in hopes of capitalizing on our naivite?