We present AlphaApollo, an agentic reasoning system that targets two bottlenecks in foundation-model reasoning: (1) limited reasoning capacity for complex, long-horizon problem solving and (2) unreliable test-time evolution without trustworthy verification. AlphaApollo orchestrates models and tools via three components: (i) multi-turn agentic reasoning, which formalizes model-environment interaction with structured tool calls and responses; (ii) multi-turn agentic learning, which applies turn-level reinforcement learning to optimize tool-use reasoning while decoupling actions from tool responses for stable training; and (iii) multi-round agentic evolution, which refines solutions through a propose-judge-update loop with tool-assisted verifications and long-horizon memory. Across seven math reasoning benchmarks and multiple model scales, AlphaApollo improves performance through reliable tool use (> 85% tool-call success), substantial gains from multi-turn RL (Avg@32: Qwen2.5-1.5B-Instruct 1.07% -> 9.64%, Qwen2.5-7B-Instruct 8.77% -> 20.35%), and improvements from evolution (e.g., Qwen2.5-3B-Instruct 5.27% -> 7.70%, Qwen2.5-14B-Instruct 16.53% -> 21.08%). This project is still ongoing. We welcome feedback from the community and will frequently update the source code and technical report.