as the title says, I wanted to ask about mathematics textbooks that are both written recently and are comprehensive. This post What books must every math undergraduate read? has a bunch of good suggestions, but many of the textbooks are quite old. Time has taken its toll on many older the books, where standard notation and presentation has changed a fair amount. For example, recent books aren't really written as terse as Rudin, and manifolds are generally defined as sets with some properties instead of subsets of some $\mathbb{R}^n$ like in Guillemin and Pollack. In the following paragraph, I will give my suggestions for textbooks.
For point set topology, differential topology, and Riemannian geometry, I suggest the manifolds trilogy by Lee. That is: Introduction to Topological Manifolds, Introduction to Smooth Manifolds, and Introduction to Riemannian Manifolds, all by Lee. Tu's books on manifolds and Riemannian geometry are contenders in this, but Lee is more comprehensive than those. For a first linear algebra textbook, I suggest Linear Algebra Done Right by Axler.
I would like to suggest Understanding Analysis by Abbott and Functions of Several Real Variables by Moskowitz and Paliogiannis to this list for single and multivariable real analysis respectively, but when compared to a book like Rudin they are considerably less comprehensive.
