This is a joint work with V.~Kurlin. We develop the Dynnikov method of three-page embeddings for {\it links with singularities} of the following type: with possible double points of intersection in general position. Let $SK$ be a semi-group with 15 generators from the alphabet ${\bf A}=\{ a_i,b_i,c_i,d_i,x_i,\; i\in {\bf Z}_3 \}$ and 84 relations: $$\begin{array}{l} (1) \quad a_i = a_{i+1} d_{i-1}, \quad b_i = a_{i-1} c_{i+1}, \quad c_i = b_{i-1} c_{i+1}, \quad d_i = a_{i+1} c_{i-1}, \\

(2) \quad x_i = d_{i+1}x_{i-1}b_{i+1}, \\

(3) \quad d_1 d_2 d_3 = 1, \\

(4) \quad b_i d_i = d_i b_i =1, \\

(5) \quad d_i x_i d_i = a_i (d_i x_i d_i) c_i, \quad b_i x_i b_i = a_i (b_i x_i b_i) c_i, \\

(6) \quad x_i (d_{i+1} d_i d_{i-1}) = (d_{i+1} d_i d_{i-1}) x_i, \\

(7) \quad (d_{i} c_{i}) w = w (d_{i} c_{i}), \mbox{ where } w\in \{c_{i+1}, x_{i+1}, b_{i} d_{i+1} d_{i} \},\\

(8) \quad (a_{i} b_{i}) w = w (a_{i} b_{i}), \mbox{ where } w\in \{a_{i+1}, b_{i+1}, c_{i+1}, x_{i+1}, b_{i} d_{i+1} d_{i} \},\\

(9) \quad t_i w = w t_i, \mbox{ where } t_i = b_{i+1} d_{i-1} d_{i+1} b_{i-1} , w\in \{ a_i, b_i, c_i, x_i, b_{i-1} d_i d_{i-1} \}, \\

(10) \quad (d_i x_i b_i) w = w (d_i x_i b_i), \mbox{ where } w\in \{a_{i+1}, b_{i+1}, c_{i+1}, x_{i+1}, b_{i} d_{i+1} d_{i} \}. \end{array} $$

\medskip \noindent {\bf Theorem 1.} {\it Every singular knot can be represented by an element of the semi-group $SK$. Two singular knots are ambient isotopic if and only if the corresponding elements of $SK$ are equal. An arbitrary element of $SK$ corresponds to a singular knot if and only if this element is central, i.e. it commutes with every element of $SK$. }