diff --git a/src/SUMMARY.md b/src/SUMMARY.md
index ceaf1af..0115cfe 100644
--- a/src/SUMMARY.md
+++ b/src/SUMMARY.md
@@ -1,3 +1,3 @@
 # Summary
 
-- [tf优化器](./chapter_1.md)
+- [TF优化器](./optimizer.md)
diff --git a/src/chapter_1.md b/src/optimizer.md
similarity index 75%
rename from src/chapter_1.md
rename to src/optimizer.md
index 3ec712e..caab891 100644
--- a/src/chapter_1.md
+++ b/src/optimizer.md
@@ -1,7 +1,26 @@
-# tf优化器
+# TF优化器
+
+`tensorflow`中优化器类继承自`optimizer.Optimizer` 
+```python
+def apply_gradients(self, grads_and_vars, global_step=None, name=None):
+    ...
+```
+该方法的默认实现与优化器类型无关，子类可以复写以下方法改变具体行为：
+```python
+  def _create_slots():
+    ...
+  def _prepare():
+    ...
+  def _apply_dense():
+    ...
+  def _apply_sparse():
+    ...
+```
 
 ## ADAM优化器
 
+Adam - A Method for Stochastic Optimization: [Kingma et al., 2015](https://arxiv.org/abs/1412.6980) ([pdf](https://arxiv.org/pdf/1412.6980.pdf))
+
 初始化
 
 $$m_0 := 0 \text{(Initialize initial 1st moment vector)}$$
@@ -17,10 +36,12 @@ $$m_t := \beta_1 * m_{t-1} + (1 - \beta_1) * g$$
 $$v_t := \beta_2 * v_{t-1} + (1 - \beta_2) * g^2$$
 $$\text{variable} := \text{variable} - \text{lr}_t * m_t / (\sqrt{v_t} + \epsilon)$$
 
+`tensorflow`中实现了`Adam`优化器，具体实现逻辑如下：
 
 [tensorflow 源码](https://github.com/tensorflow/tensorflow/blob/80b1605dbc7ac2f475dff03b13d7efcf295d35c4/tensorflow/python/training/adam.py#L247)
 ```python
 def _apply_sparse_shared(self, grad, var, indices, scatter_add):
+    # 主要计算逻辑
     beta1_power, beta2_power = self._get_beta_accumulators()
     beta1_power = math_ops.cast(beta1_power, var.dtype.base_dtype)
     beta2_power = math_ops.cast(beta2_power, var.dtype.base_dtype)
@@ -43,4 +64,4 @@ def _apply_sparse_shared(self, grad, var, indices, scatter_add):
     var_update = state_ops.assign_sub(
         var, lr * m_t / (v_sqrt + epsilon_t), use_locking=self._use_locking)
     return control_flow_ops.group(*[var_update, m_t, v_t])
-```
\ No newline at end of file
+```