You have a problem with your network addresses and masks. All the interfaces are assigned to the same network, but a router needs to have a different network on each interface (routers route between networks). There are a couple of ways to handle this. Most people use /30
networks for point-to-point links, but RFC 3021, Using 31-Bit Prefixes on IPv4 Point-to-Point Links allows you to use /31
networks (not all devices support this, but Cisco does).
With /30
networks:
R1:
interface Serial0/0/0
description to R3 S0/0/0
ip address 10.0.0.1 255.255.255.252
!
interface Serial0/1/0
description to R2 S0/0/0
ip address 10.0.0.5 255.255.255.252
!
R2:
interface Serial0/0/0
description to R1 S0/1/0
ip address 10.0.0.6 255.255.255.252
!
R3:
interface Serial0/0/0
description to R1 S0/0/0
ip address 10.0.0.2 255.255.255.252
!
With /31
networks:
R1:
interface Serial0/0/0
description to R3 S0/0/0
ip address 10.0.0.0 255.255.255.254
!
interface Serial0/1/0
description to R2 S0/0/0
ip address 10.0.0.2 255.255.255.254
!
R2:
interface Serial0/0/0
description to R1 S0/1/0
ip address 10.0.0.3 255.255.255.254
!
R3:
interface Serial0/0/0
description to R1 S0/0/0
ip address 10.0.0.1 255.255.255.254
!
You would also need for R2 and R3 to know about the networks on the other side of R1 from them. You can either use static routes (which don't scale), or you can run a routing protocol among your routers.
For example, on R2 you can place a static route to the R1 S0/0/0 network, and on R3, a static route to the R1 S0/1/0 network:
ip route <remote network address> <remote network mask> <next hop (R1) address>
R1 inherently knows about both networks because it is directly connected to both, but R2 has no way to know where to send traffic for the R1-to-R3 network, nor does R3 have any way to know about the R1-to-R2 network, unless you somehow tell those routers about the other networks. In fact, you could cheat, and use default routes:
ip route 0.0.0.0 0.0.0.0 <next hop (R1) address>