This is an early and interesting razor. It's a Gillette Milady Decollette. From the serial number (C664611) we can see it's from early 1915, the introduction year of the model. Although created as a womans model, it's about a perfect travel razor for anyone. The handle is somewhat longer than many travel razors. The "French Ivory" (celluloid) case has a broken hinge, but still keeps everything together. In spite of the age and size, the razor will use any standard Gillette style razor blade. These are available in a variety of brands in many stores and online.
As you can see in the photos, this razor set is in good, but not perfect, condition. There is some mild brassing on the razor and the blade box. As noted, the hinge on the case is broken, but the celluloid looks great. The liner has some issues, but still looks good and protects the razor well. As with many (if not most) razors of this age, there is a crack in the handle. However, it's still snug and not nearly as apparent as it looks in the photos. I didn't see it until I'd run the razor through our standard "light clean and sterilize" process. The teeth on the head are all present and straight.
Overall a very nice razor to take on trips, use at home, or display.